Connectivity is a Poor Indicator of Fast Quantum Search

NASA Astrophysics Data System (ADS)

Meyer, David A.; Wong, Thomas G.

2015-03-01

A randomly walking quantum particle evolving by Schrödinger's equation searches on d -dimensional cubic lattices in O (√{N }) time when d ≥5 , and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

NASA Astrophysics Data System (ADS)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.

PubMed

Guturu, Parthasarathy; Dantu, Ram

2008-06-01

Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.

Design of a flexible component gathering algorithm for converting cell-based models to graph representations for use in evolutionary search

PubMed Central

2014-01-01

Background The ability of science to produce experimental data has outpaced the ability to effectively visualize and integrate the data into a conceptual framework that can further higher order understanding. Multidimensional and shape-based observational data of regenerative biology presents a particularly daunting challenge in this regard. Large amounts of data are available in regenerative biology, but little progress has been made in understanding how organisms such as planaria robustly achieve and maintain body form. An example of this kind of data can be found in a new repository (PlanformDB) that encodes descriptions of planaria experiments and morphological outcomes using a graph formalism. Results We are developing a model discovery framework that uses a cell-based modeling platform combined with evolutionary search to automatically search for and identify plausible mechanisms for the biological behavior described in PlanformDB. To automate the evolutionary search we developed a way to compare the output of the modeling platform to the morphological descriptions stored in PlanformDB. We used a flexible connected component algorithm to create a graph representation of the virtual worm from the robust, cell-based simulation data. These graphs can then be validated and compared with target data from PlanformDB using the well-known graph-edit distance calculation, which provides a quantitative metric of similarity between graphs. The graph edit distance calculation was integrated into a fitness function that was able to guide automated searches for unbiased models of planarian regeneration. We present a cell-based model of planarian that can regenerate anatomical regions following bisection of the organism, and show that the automated model discovery framework is capable of searching for and finding models of planarian regeneration that match experimental data stored in PlanformDB. Conclusion The work presented here, including our algorithm for converting cell-based models into graphs for comparison with data stored in an external data repository, has made feasible the automated development, training, and validation of computational models using morphology-based data. This work is part of an ongoing project to automate the search process, which will greatly expand our ability to identify, consider, and test biological mechanisms in the field of regenerative biology. PMID:24917489

Application of Metaheuristic and Deterministic Algorithms for Aircraft Reference Trajectory Optimization =

NASA Astrophysics Data System (ADS)

Murrieta Mendoza, Alejandro

Aircraft reference trajectory is an alternative method to reduce fuel consumption, thus the pollution released to the atmosphere. Fuel consumption reduction is of special importance for two reasons: first, because the aeronautical industry is responsible of 2% of the CO2 released to the atmosphere, and second, because it will reduce the flight cost. The aircraft fuel model was obtained from a numerical performance database which was created and validated by our industrial partner from flight experimental test data. A new methodology using the numerical database was proposed in this thesis to compute the fuel burn for a given trajectory. Weather parameters such as wind and temperature were taken into account as they have an important effect in fuel burn. The open source model used to obtain the weather forecast was provided by Weather Canada. A combination of linear and bi-linear interpolations allowed finding the required weather data. The search space was modelled using different graphs: one graph was used for mapping the different flight phases such as climb, cruise and descent, and another graph was used for mapping the physical space in which the aircraft would perform its flight. The trajectory was optimized in its vertical reference trajectory using the Beam Search algorithm, and a combination of the Beam Search algorithm with a search space reduction technique. The trajectory was optimized simultaneously for the vertical and lateral reference navigation plans while fulfilling a Required Time of Arrival constraint using three different metaheuristic algorithms: the artificial bee's colony, and the ant colony optimization. Results were validated using the software FlightSIMRTM, a commercial Flight Management System, an exhaustive search algorithm, and as flown flights obtained from flightawareRTM. All algorithms were able to reduce the fuel burn, and the flight costs. None None None None None None None

Graph 500 on OpenSHMEM: Using a Practical Survey of Past Work to Motivate Novel Algorithmic Developments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grossman, Max; Pritchard Jr., Howard Porter; Budimlic, Zoran

2016-12-22

Graph500 [14] is an effort to offer a standardized benchmark across large-scale distributed platforms which captures the behavior of common communicationbound graph algorithms. Graph500 differs from other large-scale benchmarking efforts (such as HPL [6] or HPGMG [7]) primarily in the irregularity of its computation and data access patterns. The core computational kernel of Graph500 is a breadth-first search (BFS) implemented on an undirected graph. The output of Graph500 is a spanning tree of the input graph, usually represented by a predecessor mapping for every node in the graph. The Graph500 benchmark defines several pre-defined input sizes for implementers to testmore » against. This report summarizes investigation into implementing the Graph500 benchmark on OpenSHMEM, and focuses on first building a strong and practical understanding of the strengths and limitations of past work before proposing and developing novel extensions.« less

Image processing meta-algorithm development via genetic manipulation of existing algorithm graphs

NASA Astrophysics Data System (ADS)

Schalkoff, Robert J.; Shaaban, Khaled M.

1999-07-01

Automatic algorithm generation for image processing applications is not a new idea, however previous work is either restricted to morphological operates or impractical. In this paper, we show recent research result in the development and use of meta-algorithms, i.e. algorithms which lead to new algorithms. Although the concept is generally applicable, the application domain in this work is restricted to image processing. The meta-algorithm concept described in this paper is based upon out work in dynamic algorithm. The paper first present the concept of dynamic algorithms which, on the basis of training and archived algorithmic experience embedded in an algorithm graph (AG), dynamically adjust the sequence of operations applied to the input image data. Each node in the tree-based representation of a dynamic algorithm with out degree greater than 2 is a decision node. At these nodes, the algorithm examines the input data and determines which path will most likely achieve the desired results. This is currently done using nearest-neighbor classification. The details of this implementation are shown. The constrained perturbation of existing algorithm graphs, coupled with a suitable search strategy, is one mechanism to achieve meta-algorithm an doffers rich potential for the discovery of new algorithms. In our work, a meta-algorithm autonomously generates new dynamic algorithm graphs via genetic recombination of existing algorithm graphs. The AG representation is well suited to this genetic-like perturbation, using a commonly- employed technique in artificial neural network synthesis, namely the blueprint representation of graphs. A number of exam. One of the principal limitations of our current approach is the need for significant human input in the learning phase. Efforts to overcome this limitation are discussed. Future research directions are indicated.

Restarting and recentering genetic algorithm variations for DNA fragment assembly: The necessity of a multi-strategy approach.

PubMed

Hughes, James Alexander; Houghten, Sheridan; Ashlock, Daniel

2016-12-01

DNA Fragment assembly - an NP-Hard problem - is one of the major steps in of DNA sequencing. Multiple strategies have been used for this problem, including greedy graph-based algorithms, deBruijn graphs, and the overlap-layout-consensus approach. This study focuses on the overlap-layout-consensus approach. Heuristics and computational intelligence methods are combined to exploit their respective benefits. These algorithm combinations were able to produce high quality results surpassing the best results obtained by a number of competitive algorithms specially designed and tuned for this problem on thirteen of sixteen popular benchmarks. This work also reinforces the necessity of using multiple search strategies as it is clearly observed that algorithm performance is dependent on problem instance; without a deeper look into many searches, top solutions could be missed entirely. Copyright © 2016. Published by Elsevier Ireland Ltd.

Output-Sensitive Construction of Reeb Graphs.

PubMed

Doraiswamy, H; Natarajan, V

2012-01-01

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Critical points correspond to nodes in the Reeb graph. Arcs connecting the nodes are computed in the second step by a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. Finally, the Reeb graph is employed in four different applications-surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data.

Asymmetry in search.

PubMed

Kaindl, H; Kainz, G; Radda, K

2001-01-01

Most of the work on search in artificial intelligence (AI) deals with one search direction only-mostly forward search-although it is known that a structural asymmetry of the search graph causes differences in the efficiency of searching in the forward or the backward direction, respectively. In the case of symmetrical graph structure, however, current theory would not predict such differences in efficiency. In several classes of job sequencing problems, we observed a phenomenon of asymmetry in search that relates to the distribution of the are costs in the search graph. This phenomenon can be utilized for improving the search efficiency by a new algorithm that automatically selects the search direction. We demonstrate fur a class of job sequencing problems that, through the utilization of this phenomenon, much more difficult problems can be solved-according to our best knowledge-than by the best published approach, and on the same problems, the running time is much reduced. As a consequence, we propose to check given problems for asymmetrical distribution of are costs that may cause asymmetry in search.

Stationary states in quantum walk search

NASA Astrophysics Data System (ADS)

PrÅ«sis, Krišjānis; Vihrovs, Jevgěnijs; Wong, Thomas G.

2016-09-01

When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by causing the system to approximately begin in a stationary state, so the system fails to evolve. In this paper, we completely characterize the stationary states, or 1-eigenvectors, of the quantum walk search operator for general graphs and configurations of marked vertices by decomposing their amplitudes into uniform and flip states. This infinitely expands the number of known stationary states and gives an optimization procedure to find the stationary state closest to the initial uniform state of the walk. We further prove theorems on the existence of stationary states, with them conditionally existing if the marked vertices form a bipartite connected component and always existing if nonbipartite. These results utilize the standard oracle in Grover's algorithm, but we show that a different type of oracle prevents stationary states from interfering with the search algorithm.

The PANTHER User Experience

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coram, Jamie L.; Morrow, James D.; Perkins, David Nikolaus

2015-09-01

This document describes the PANTHER R&D Application, a proof-of-concept user interface application developed under the PANTHER Grand Challenge LDRD. The purpose of the application is to explore interaction models for graph analytics, drive algorithmic improvements from an end-user point of view, and support demonstration of PANTHER technologies to potential customers. The R&D Application implements a graph-centric interaction model that exposes analysts to the algorithms contained within the GeoGraphy graph analytics library. Users define geospatial-temporal semantic graph queries by constructing search templates based on nodes, edges, and the constraints among them. Users then analyze the results of the queries using bothmore » geo-spatial and temporal visualizations. Development of this application has made user experience an explicit driver for project and algorithmic level decisions that will affect how analysts one day make use of PANTHER technologies.« less

Optimal Fungal Space Searching Algorithms.

PubMed

Asenova, Elitsa; Lin, Hsin-Yu; Fu, Eileen; Nicolau, Dan V; Nicolau, Dan V

2016-10-01

Previous experiments have shown that fungi use an efficient natural algorithm for searching the space available for their growth in micro-confined networks, e.g., mazes. This natural "master" algorithm, which comprises two "slave" sub-algorithms, i.e., collision-induced branching and directional memory, has been shown to be more efficient than alternatives, with one, or the other, or both sub-algorithms turned off. In contrast, the present contribution compares the performance of the fungal natural algorithm against several standard artificial homologues. It was found that the space-searching fungal algorithm consistently outperforms uninformed algorithms, such as Depth-First-Search (DFS). Furthermore, while the natural algorithm is inferior to informed ones, such as A*, this under-performance does not importantly increase with the increase of the size of the maze. These findings suggest that a systematic effort of harvesting the natural space searching algorithms used by microorganisms is warranted and possibly overdue. These natural algorithms, if efficient, can be reverse-engineered for graph and tree search strategies.

Search and Graph Database Technologies for Biomedical Semantic Indexing: Experimental Analysis.

PubMed

Segura Bedmar, Isabel; Martínez, Paloma; Carruana Martín, Adrián

2017-12-01

Biomedical semantic indexing is a very useful support tool for human curators in their efforts for indexing and cataloging the biomedical literature. The aim of this study was to describe a system to automatically assign Medical Subject Headings (MeSH) to biomedical articles from MEDLINE. Our approach relies on the assumption that similar documents should be classified by similar MeSH terms. Although previous work has already exploited the document similarity by using a k-nearest neighbors algorithm, we represent documents as document vectors by search engine indexing and then compute the similarity between documents using cosine similarity. Once the most similar documents for a given input document are retrieved, we rank their MeSH terms to choose the most suitable set for the input document. To do this, we define a scoring function that takes into account the frequency of the term into the set of retrieved documents and the similarity between the input document and each retrieved document. In addition, we implement guidelines proposed by human curators to annotate MEDLINE articles; in particular, the heuristic that says if 3 MeSH terms are proposed to classify an article and they share the same ancestor, they should be replaced by this ancestor. The representation of the MeSH thesaurus as a graph database allows us to employ graph search algorithms to quickly and easily capture hierarchical relationships such as the lowest common ancestor between terms. Our experiments show promising results with an F1 of 69% on the test dataset. To the best of our knowledge, this is the first work that combines search and graph database technologies for the task of biomedical semantic indexing. Due to its horizontal scalability, ElasticSearch becomes a real solution to index large collections of documents (such as the bibliographic database MEDLINE). Moreover, the use of graph search algorithms for accessing MeSH information could provide a support tool for cataloging MEDLINE abstracts in real time. ©Isabel Segura Bedmar, Paloma Martínez, Adrián Carruana Martín. Originally published in JMIR Medical Informatics (http://medinform.jmir.org), 01.12.2017.

Automated intraretinal layer segmentation of optical coherence tomography images using graph-theoretical methods

NASA Astrophysics Data System (ADS)

Roy, Priyanka; Gholami, Peyman; Kuppuswamy Parthasarathy, Mohana; Zelek, John; Lakshminarayanan, Vasudevan

2018-02-01

Segmentation of spectral-domain Optical Coherence Tomography (SD-OCT) images facilitates visualization and quantification of sub-retinal layers for diagnosis of retinal pathologies. However, manual segmentation is subjective, expertise dependent, and time-consuming, which limits applicability of SD-OCT. Efforts are therefore being made to implement active-contours, artificial intelligence, and graph-search to automatically segment retinal layers with accuracy comparable to that of manual segmentation, to ease clinical decision-making. Although, low optical contrast, heavy speckle noise, and pathologies pose challenges to automated segmentation. Graph-based image segmentation approach stands out from the rest because of its ability to minimize the cost function while maximising the flow. This study has developed and implemented a shortest-path based graph-search algorithm for automated intraretinal layer segmentation of SD-OCT images. The algorithm estimates the minimal-weight path between two graph-nodes based on their gradients. Boundary position indices (BPI) are computed from the transition between pixel intensities. The mean difference between BPIs of two consecutive layers quantify individual layer thicknesses, which shows statistically insignificant differences when compared to a previous study [for overall retina: p = 0.17, for individual layers: p > 0.05 (except one layer: p = 0.04)]. These results substantiate the accurate delineation of seven intraretinal boundaries in SD-OCT images by this algorithm, with a mean computation time of 0.93 seconds (64-bit Windows10, core i5, 8GB RAM). Besides being self-reliant for denoising, the algorithm is further computationally optimized to restrict segmentation within the user defined region-of-interest. The efficiency and reliability of this algorithm, even in noisy image conditions, makes it clinically applicable.

AND/OR graph representation of assembly plans

NASA Astrophysics Data System (ADS)

Homem de Mello, Luiz S.; Sanderson, Arthur C.

1990-04-01

A compact representation of all possible assembly plans of a product using AND/OR graphs is presented as a basis for efficient planning algorithms that allow an intelligent robot to pick a course of action according to instantaneous conditions. The AND/OR graph is equivalent to a state transition graph but requires fewer nodes and simplifies the search for feasible plans. Three applications are discussed: (1) the preselection of the best assembly plan, (2) the recovery from execution errors, and (3) the opportunistic scheduling of tasks. An example of an assembly with four parts illustrates the use of the AND/OR graph representation in assembly-plan preselection, based on the weighting of operations according to complexity of manipulation and stability of subassemblies. A hypothetical error situation is discussed to show how a bottom-up search of the AND/OR graph leads to an efficient recovery.

AND/OR graph representation of assembly plans

NASA Technical Reports Server (NTRS)

Homem De Mello, Luiz S.; Sanderson, Arthur C.

1990-01-01

A compact representation of all possible assembly plans of a product using AND/OR graphs is presented as a basis for efficient planning algorithms that allow an intelligent robot to pick a course of action according to instantaneous conditions. The AND/OR graph is equivalent to a state transition graph but requires fewer nodes and simplifies the search for feasible plans. Three applications are discussed: (1) the preselection of the best assembly plan, (2) the recovery from execution errors, and (3) the opportunistic scheduling of tasks. An example of an assembly with four parts illustrates the use of the AND/OR graph representation in assembly-plan preselection, based on the weighting of operations according to complexity of manipulation and stability of subassemblies. A hypothetical error situation is discussed to show how a bottom-up search of the AND/OR graph leads to an efficient recovery.

Tractable Algorithms for Proximity Search on Large Graphs

DTIC Science & Technology

2010-07-01

development in information retrieval, 2005. 5.1 164 A. K. Chandra, P. Raghavan, W. L. Ruzzo, and R. Smolensky. The electrical resistance of a graph captures...2007] show how to use hitting times for designing provably manipulation resistant reputation systems. Harmonic func- tions have been used for...commute times with electrical net- works (Doyle and Snell [1984]). Consider an undirected graph. Now think of each edge as a resistor with conductance

Design tool for multiprocessor scheduling and evaluation of iterative dataflow algorithms

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1995-01-01

A graph-theoretic design process and software tool is defined for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described with a dataflow graph and are intended to be executed repetitively on a set of identical processors. Typical applications include signal processing and control law problems. Graph-search algorithms and analysis techniques are introduced and shown to effectively determine performance bounds, scheduling constraints, and resource requirements. The software tool applies the design process to a given problem and includes performance optimization through the inclusion of additional precedence constraints among the schedulable tasks.

Finding paths in tree graphs with a quantum walk

NASA Astrophysics Data System (ADS)

Koch, Daniel; Hillery, Mark

2018-01-01

We analyze the potential for different types of searches using the formalism of scattering random walks on quantum computers. Given a particular type of graph consisting of nodes and connections, a "tree maze," we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both through numerical calculations as well as by using the eigenvectors and eigenvalues of the quantum system.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Spatial search on a two-dimensional lattice with long-range interactions

NASA Astrophysics Data System (ADS)

Osada, Tomo; Sanaka, Kaoru; Munro, William J.; Nemoto, Kae

2018-06-01

Quantum-walk-based algorithms that search a marked location among N locations on a d -dimensional lattice succeeds in time O (√{N }) for d >2 , while this is not found to be possible when d =2 . In this paper, we consider a spatial search algorithm using continuous-time quantum walk on a two-dimensional square lattice with the existence of additional long-range edges. We examined such a search on a probabilistic graph model where an edge connecting non-nearest-neighbor lattice points i and j apart by a distance |i -j | is added by probability pi j=|i-j | -α(α ≥0 ) . Through numerical analysis, we found that the search succeeds in time O (√{N }) when α ≤αc=2.4 ±0.1 . For α >2 , the expectation value of the additional long-range edges on each node scales as a constant when N →∞ , which means that search time of O (√{N }) is achieved on a graph with average degree scaling as a constant.

A novel adaptive Cuckoo search for optimal query plan generation.

PubMed

Gomathi, Ramalingam; Sharmila, Dhandapani

2014-01-01

The emergence of multiple web pages day by day leads to the development of the semantic web technology. A World Wide Web Consortium (W3C) standard for storing semantic web data is the resource description framework (RDF). To enhance the efficiency in the execution time for querying large RDF graphs, the evolving metaheuristic algorithms become an alternate to the traditional query optimization methods. This paper focuses on the problem of query optimization of semantic web data. An efficient algorithm called adaptive Cuckoo search (ACS) for querying and generating optimal query plan for large RDF graphs is designed in this research. Experiments were conducted on different datasets with varying number of predicates. The experimental results have exposed that the proposed approach has provided significant results in terms of query execution time. The extent to which the algorithm is efficient is tested and the results are documented.

Equivalence of Szegedy's and coined quantum walks

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-09-01

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

SING: Subgraph search In Non-homogeneous Graphs

PubMed Central

2010-01-01

Background Finding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs. Results In this paper, SING (Subgraph search In Non-homogeneous Graphs), a novel indexing system able to cope with large graphs, is presented. The method uses the notion of feature, which can be a small subgraph, subtree or path. Each graph in the database is annotated with the set of all its features. The key point is to make use of feature locality information. This idea is used to both improve the filtering performance and speed up the subgraph isomorphism task. Conclusions Extensive tests on chemical compounds, biological networks and synthetic graphs show that the proposed system outperforms the most popular systems in query time over databases of medium and large graphs. Other specific tests show that the proposed system is effective for single large graphs. PMID:20170516

Decomposition Algorithm for Global Reachability on a Time-Varying Graph

NASA Technical Reports Server (NTRS)

Kuwata, Yoshiaki

2010-01-01

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

Monkey search algorithm for ECE components partitioning

NASA Astrophysics Data System (ADS)

Kuliev, Elmar; Kureichik, Vladimir; Kureichik, Vladimir, Jr.

2018-05-01

The paper considers one of the important design problems – a partitioning of electronic computer equipment (ECE) components (blocks). It belongs to the NP-hard class of problems and has a combinatorial and logic nature. In the paper, a partitioning problem formulation can be found as a partition of graph into parts. To solve the given problem, the authors suggest using a bioinspired approach based on a monkey search algorithm. Based on the developed software, computational experiments were carried out that show the algorithm efficiency, as well as its recommended settings for obtaining more effective solutions in comparison with a genetic algorithm.

Planning Robot-Control Parameters With Qualitative Reasoning

NASA Technical Reports Server (NTRS)

Peters, Stephen F.

1993-01-01

Qualitative-reasoning planning algorithm helps to determine quantitative parameters controlling motion of robot. Algorithm regarded as performing search in multidimensional space of control parameters from starting point to goal region in which desired result of robotic manipulation achieved. Makes use of directed graph representing qualitative physical equations describing task, and interacts, at each sampling period, with history of quantitative control parameters and sensory data, to narrow search for reliable values of quantitative control parameters.

Tree decomposition based fast search of RNA structures including pseudoknots in genomes.

PubMed

Song, Yinglei; Liu, Chunmei; Malmberg, Russell; Pan, Fangfang; Cai, Liming

2005-01-01

Searching genomes for RNA secondary structure with computational methods has become an important approach to the annotation of non-coding RNAs. However, due to the lack of efficient algorithms for accurate RNA structure-sequence alignment, computer programs capable of fast and effectively searching genomes for RNA secondary structures have not been available. In this paper, a novel RNA structure profiling model is introduced based on the notion of a conformational graph to specify the consensus structure of an RNA family. Tree decomposition yields a small tree width t for such conformation graphs (e.g., t = 2 for stem loops and only a slight increase for pseudo-knots). Within this modelling framework, the optimal alignment of a sequence to the structure model corresponds to finding a maximum valued isomorphic subgraph and consequently can be accomplished through dynamic programming on the tree decomposition of the conformational graph in time O(k(t)N(2)), where k is a small parameter; and N is the size of the projiled RNA structure. Experiments show that the application of the alignment algorithm to search in genomes yields the same search accuracy as methods based on a Covariance model with a significant reduction in computation time. In particular; very accurate searches of tmRNAs in bacteria genomes and of telomerase RNAs in yeast genomes can be accomplished in days, as opposed to months required by other methods. The tree decomposition based searching tool is free upon request and can be downloaded at our site h t t p ://w.uga.edu/RNA-informatics/software/index.php.

Expert system validation in prolog

NASA Technical Reports Server (NTRS)

Stock, Todd; Stachowitz, Rolf; Chang, Chin-Liang; Combs, Jacqueline

1988-01-01

An overview of the Expert System Validation Assistant (EVA) is being implemented in Prolog at the Lockheed AI Center. Prolog was chosen to facilitate rapid prototyping of the structure and logic checkers and since February 1987, we have implemented code to check for irrelevance, subsumption, duplication, deadends, unreachability, and cycles. The architecture chosen is extremely flexible and expansible, yet concise and complementary with the normal interactive style of Prolog. The foundation of the system is in the connection graph representation. Rules and facts are modeled as nodes in the graph and arcs indicate common patterns between rules. The basic activity of the validation system is then a traversal of the connection graph, searching for various patterns the system recognizes as erroneous. To aid in specifying these patterns, a metalanguage is developed, providing the user with the basic facilities required to reason about the expert system. Using the metalanguage, the user can, for example, give the Prolog inference engine the goal of finding inconsistent conclusions among the rules, and Prolog will search the graph intantiations which can match the definition of inconsistency. Examples of code for some of the checkers are provided and the algorithms explained. Technical highlights include automatic construction of a connection graph, demonstration of the use of metalanguage, the A* algorithm modified to detect all unique cycles, general-purpose stacks in Prolog, and a general-purpose database browser with pattern completion.

The Fragment Network: A Chemistry Recommendation Engine Built Using a Graph Database.

PubMed

Hall, Richard J; Murray, Christopher W; Verdonk, Marcel L

2017-07-27

The hit validation stage of a fragment-based drug discovery campaign involves probing the SAR around one or more fragment hits. This often requires a search for similar compounds in a corporate collection or from commercial suppliers. The Fragment Network is a graph database that allows a user to efficiently search chemical space around a compound of interest. The result set is chemically intuitive, naturally grouped by substitution pattern and meaningfully sorted according to the number of observations of each transformation in medicinal chemistry databases. This paper describes the algorithms used to construct and search the Fragment Network and provides examples of how it may be used in a drug discovery context.

Erratum: Erratum: Denoising Phase Unwrapping Algorithm for Precise Phase Shifting Interferometry

NASA Astrophysics Data System (ADS)

Phuc, Phan Huy; Rhee, Hyug-Gyo; Ghim, Young-Sik

2018-06-01

This is a revision of the reference list reported in the original article. In order to clear the contribution of the previous work on the incremental breadth-first search (IBFS) method applied to the PUMA algorithm, we add one more reference to the existing reference list, as in this erratum. Page 83 : In this paper, we propose an algorithm that modifies the Boykov-Kolmogorov (BK) algorithm using the incremental breadth-first search (IBFS) method [27, 28] to find paths from the source to the sink of a graph. [28] S. Ali, H. Khan, I. Shaik and F. Ali, Int. J. Eng. and Technol. 7, 254 (2015).

Mixing times in quantum walks on two-dimensional grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-15

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and themore » running time of the corresponding abstract search algorithm is discussed.« less

Mixing times in quantum walks on two-dimensional grids

NASA Astrophysics Data System (ADS)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-01

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.

Estimating Causal Effects with Ancestral Graph Markov Models

PubMed Central

Malinsky, Daniel; Spirtes, Peter

2017-01-01

We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present. PMID:28217244

A technology mapping based on graph of excitations and outputs for finite state machines

NASA Astrophysics Data System (ADS)

Kania, Dariusz; Kulisz, Józef

2017-11-01

A new, efficient technology mapping method of FSMs, dedicated for PAL-based PLDs is proposed. The essence of the method consists in searching for the minimal set of PAL-based logic blocks that cover a set of multiple-output implicants describing the transition and output functions of an FSM. The method is based on a new concept of graph: the Graph of Excitations and Outputs. The proposed algorithm was tested using the FSM benchmarks. The obtained results were compared with the classical technology mapping of FSM.

Object recognition in images via a factor graph model

NASA Astrophysics Data System (ADS)

He, Yong; Wang, Long; Wu, Zhaolin; Zhang, Haisu

2018-04-01

Object recognition in images suffered from huge search space and uncertain object profile. Recently, the Bag-of- Words methods are utilized to solve these problems, especially the 2-dimension CRF(Conditional Random Field) model. In this paper we suggest the method based on a general and flexible fact graph model, which can catch the long-range correlation in Bag-of-Words by constructing a network learning framework contrasted from lattice in CRF. Furthermore, we explore a parameter learning algorithm based on the gradient descent and Loopy Sum-Product algorithms for the factor graph model. Experimental results on Graz 02 dataset show that, the recognition performance of our method in precision and recall is better than a state-of-art method and the original CRF model, demonstrating the effectiveness of the proposed method.

Scalable Matrix Algorithms for Interactive Analytics of Very Large Informatics Graphs

DTIC Science & Technology

2017-06-14

information networks. Depending on the situation, these larger networks may not fit on a single machine. Although we considered traditional matrix and graph...collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources...gathering and maintaining the data needed, and completing and reviewing the collection of information . Send comments regarding this burden estimate or

Computing Principal Eigenvectors of Large Web Graphs: Algorithms and Accelerations Related to PageRank and HITS

ERIC Educational Resources Information Center

Nagasinghe, Iranga

2010-01-01

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees.

PubMed

Fleischauer, Markus; Böcker, Sebastian

2018-01-01

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

Improving graph-based OCT segmentation for severe pathology in retinitis pigmentosa patients

NASA Astrophysics Data System (ADS)

Lang, Andrew; Carass, Aaron; Bittner, Ava K.; Ying, Howard S.; Prince, Jerry L.

2017-03-01

Three dimensional segmentation of macular optical coherence tomography (OCT) data of subjects with retinitis pigmentosa (RP) is a challenging problem due to the disappearance of the photoreceptor layers, which causes algorithms developed for segmentation of healthy data to perform poorly on RP patients. In this work, we present enhancements to a previously developed graph-based OCT segmentation pipeline to enable processing of RP data. The algorithm segments eight retinal layers in RP data by relaxing constraints on the thickness and smoothness of each layer learned from healthy data. Following from prior work, a random forest classifier is first trained on the RP data to estimate boundary probabilities, which are used by a graph search algorithm to find the optimal set of nine surfaces that fit the data. Due to the intensity disparity between normal layers of healthy controls and layers in various stages of degeneration in RP patients, an additional intensity normalization step is introduced. Leave-one-out validation on data acquired from nine subjects showed an average overall boundary error of 4.22 μm as compared to 6.02 μm using the original algorithm.

A Whirlwind Tour of Computational Geometry.

ERIC Educational Resources Information Center

Graham, Ron; Yao, Frances

1990-01-01

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

Information Retrieval and Graph Analysis Approaches for Book Recommendation.

PubMed

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

Information Retrieval and Graph Analysis Approaches for Book Recommendation

PubMed Central

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments. PMID:26504899

High performance genetic algorithm for VLSI circuit partitioning

NASA Astrophysics Data System (ADS)

Dinu, Simona

2016-12-01

Partitioning is one of the biggest challenges in computer-aided design for VLSI circuits (very large-scale integrated circuits). This work address the min-cut balanced circuit partitioning problem- dividing the graph that models the circuit into almost equal sized k sub-graphs while minimizing the number of edges cut i.e. minimizing the number of edges connecting the sub-graphs. The problem may be formulated as a combinatorial optimization problem. Experimental studies in the literature have shown the problem to be NP-hard and thus it is important to design an efficient heuristic algorithm to solve it. The approach proposed in this study is a parallel implementation of a genetic algorithm, namely an island model. The information exchange between the evolving subpopulations is modeled using a fuzzy controller, which determines an optimal balance between exploration and exploitation of the solution space. The results of simulations show that the proposed algorithm outperforms the standard sequential genetic algorithm both in terms of solution quality and convergence speed. As a direction for future study, this research can be further extended to incorporate local search operators which should include problem-specific knowledge. In addition, the adaptive configuration of mutation and crossover rates is another guidance for future research.

Enhanced Visualization of Subtle Outer Retinal Pathology by En Face Optical Coherence Tomography and Correlation with Multi-Modal Imaging

PubMed Central

Chew, Avenell L.; Lamey, Tina; McLaren, Terri; De Roach, John

2016-01-01

Purpose To present en face optical coherence tomography (OCT) images generated by graph-search theory algorithm-based custom software and examine correlation with other imaging modalities. Methods En face OCT images derived from high density OCT volumetric scans of 3 healthy subjects and 4 patients using a custom algorithm (graph-search theory) and commercial software (Heidelberg Eye Explorer software (Heidelberg Engineering)) were compared and correlated with near infrared reflectance, fundus autofluorescence, adaptive optics flood-illumination ophthalmoscopy (AO-FIO) and microperimetry. Results Commercial software was unable to generate accurate en face OCT images in eyes with retinal pigment epithelium (RPE) pathology due to segmentation error at the level of Bruch’s membrane (BM). Accurate segmentation of the basal RPE and BM was achieved using custom software. The en face OCT images from eyes with isolated interdigitation or ellipsoid zone pathology were of similar quality between custom software and Heidelberg Eye Explorer software in the absence of any other significant outer retinal pathology. En face OCT images demonstrated angioid streaks, lesions of acute macular neuroretinopathy, hydroxychloroquine toxicity and Bietti crystalline deposits that correlated with other imaging modalities. Conclusions Graph-search theory algorithm helps to overcome the limitations of outer retinal segmentation inaccuracies in commercial software. En face OCT images can provide detailed topography of the reflectivity within a specific layer of the retina which correlates with other forms of fundus imaging. Our results highlight the need for standardization of image reflectivity to facilitate quantification of en face OCT images and longitudinal analysis. PMID:27959968

An asynchronous traversal engine for graph-based rich metadata management

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, Dong; Carns, Philip; Ross, Robert B.

Rich metadata in high-performance computing (HPC) systems contains extended information about users, jobs, data files, and their relationships. Property graphs are a promising data model to represent heterogeneous rich metadata flexibly. Specifically, a property graph can use vertices to represent different entities and edges to record the relationships between vertices with unique annotations. The high-volume HPC use case, with millions of entities and relationships, naturally requires an out-of-core distributed property graph database, which must support live updates (to ingest production information in real time), low-latency point queries (for frequent metadata operations such as permission checking), and large-scale traversals (for provenancemore » data mining). Among these needs, large-scale property graph traversals are particularly challenging for distributed graph storage systems. Most existing graph systems implement a "level synchronous" breadth-first search algorithm that relies on global synchronization in each traversal step. This performs well in many problem domains; but a rich metadata management system is characterized by imbalanced graphs, long traversal lengths, and concurrent workloads, each of which has the potential to introduce or exacerbate stragglers (i.e., abnormally slow steps or servers in a graph traversal) that lead to low overall throughput for synchronous traversal algorithms. Previous research indicated that the straggler problem can be mitigated by using asynchronous traversal algorithms, and many graph-processing frameworks have successfully demonstrated this approach. Such systems require the graph to be loaded into a separate batch-processing framework instead of being iteratively accessed, however. In this work, we investigate a general asynchronous graph traversal engine that can operate atop a rich metadata graph in its native format. We outline a traversal-aware query language and key optimizations (traversal-affiliate caching and execution merging) necessary for efficient performance. We further explore the effect of different graph partitioning strategies on the traversal performance for both synchronous and asynchronous traversal engines. Our experiments show that the asynchronous graph traversal engine is more efficient than its synchronous counterpart in the case of HPC rich metadata processing, where more servers are involved and larger traversals are needed. Furthermore, the asynchronous traversal engine is more adaptive to different graph partitioning strategies.« less

An asynchronous traversal engine for graph-based rich metadata management

DOE PAGES

Dai, Dong; Carns, Philip; Ross, Robert B.; ...

2016-06-23

Rich metadata in high-performance computing (HPC) systems contains extended information about users, jobs, data files, and their relationships. Property graphs are a promising data model to represent heterogeneous rich metadata flexibly. Specifically, a property graph can use vertices to represent different entities and edges to record the relationships between vertices with unique annotations. The high-volume HPC use case, with millions of entities and relationships, naturally requires an out-of-core distributed property graph database, which must support live updates (to ingest production information in real time), low-latency point queries (for frequent metadata operations such as permission checking), and large-scale traversals (for provenancemore » data mining). Among these needs, large-scale property graph traversals are particularly challenging for distributed graph storage systems. Most existing graph systems implement a "level synchronous" breadth-first search algorithm that relies on global synchronization in each traversal step. This performs well in many problem domains; but a rich metadata management system is characterized by imbalanced graphs, long traversal lengths, and concurrent workloads, each of which has the potential to introduce or exacerbate stragglers (i.e., abnormally slow steps or servers in a graph traversal) that lead to low overall throughput for synchronous traversal algorithms. Previous research indicated that the straggler problem can be mitigated by using asynchronous traversal algorithms, and many graph-processing frameworks have successfully demonstrated this approach. Such systems require the graph to be loaded into a separate batch-processing framework instead of being iteratively accessed, however. In this work, we investigate a general asynchronous graph traversal engine that can operate atop a rich metadata graph in its native format. We outline a traversal-aware query language and key optimizations (traversal-affiliate caching and execution merging) necessary for efficient performance. We further explore the effect of different graph partitioning strategies on the traversal performance for both synchronous and asynchronous traversal engines. Our experiments show that the asynchronous graph traversal engine is more efficient than its synchronous counterpart in the case of HPC rich metadata processing, where more servers are involved and larger traversals are needed. Furthermore, the asynchronous traversal engine is more adaptive to different graph partitioning strategies.« less

Determination system for solar cell layout in traffic light network using dominating set

NASA Astrophysics Data System (ADS)

Eka Yulia Retnani, Windi; Fambudi, Brelyanes Z.; Slamin

2018-04-01

Graph Theory is one of the fields in Mathematics that solves discrete problems. In daily life, the applications of Graph Theory are used to solve various problems. One of the topics in the Graph Theory that is used to solve the problem is the dominating set. The concept of dominating set is used, for example, to locate some objects systematically. In this study, the dominating set are used to determine the dominating points for solar panels, where the vertex represents the traffic light point and the edge represents the connection between the points of the traffic light. To search the dominating points for solar panels using the greedy algorithm. This algorithm is used to determine the location of solar panel. This research produced applications that can determine the location of solar panels with optimal results, that is, the minimum dominating points.

A critical analysis of computational protein design with sparse residue interaction graphs

PubMed Central

Georgiev, Ivelin S.

2017-01-01

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies. PMID:28358804

A proximity-based graph clustering method for the identification and application of transcription factor clusters.

PubMed

Spadafore, Maxwell; Najarian, Kayvan; Boyle, Alan P

2017-11-29

Transcription factors (TFs) form a complex regulatory network within the cell that is crucial to cell functioning and human health. While methods to establish where a TF binds to DNA are well established, these methods provide no information describing how TFs interact with one another when they do bind. TFs tend to bind the genome in clusters, and current methods to identify these clusters are either limited in scope, unable to detect relationships beyond motif similarity, or not applied to TF-TF interactions. Here, we present a proximity-based graph clustering approach to identify TF clusters using either ChIP-seq or motif search data. We use TF co-occurrence to construct a filtered, normalized adjacency matrix and use the Markov Clustering Algorithm to partition the graph while maintaining TF-cluster and cluster-cluster interactions. We then apply our graph structure beyond clustering, using it to increase the accuracy of motif-based TFBS searching for an example TF. We show that our method produces small, manageable clusters that encapsulate many known, experimentally validated transcription factor interactions and that our method is capable of capturing interactions that motif similarity methods might miss. Our graph structure is able to significantly increase the accuracy of motif TFBS searching, demonstrating that the TF-TF connections within the graph correlate with biological TF-TF interactions. The interactions identified by our method correspond to biological reality and allow for fast exploration of TF clustering and regulatory dynamics.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

NASA Astrophysics Data System (ADS)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels

NASA Astrophysics Data System (ADS)

Havemann, Frank; Heinz, Michael; Struck, Alexander; Gläser, Jochen

2011-01-01

We propose a new local, deterministic and parameter-free algorithm that detects fuzzy and crisp overlapping communities in a weighted network and simultaneously reveals their hierarchy. Using a local fitness function, the algorithm greedily expands natural communities of seeds until the whole graph is covered. The hierarchy of communities is obtained analytically by calculating resolution levels at which communities grow rather than numerically by testing different resolution levels. This analytic procedure is not only more exact than its numerical alternatives such as LFM and GCE but also much faster. Critical resolution levels can be identified by searching for intervals in which large changes of the resolution do not lead to growth of communities. We tested our algorithm on benchmark graphs and on a network of 492 papers in information science. Combined with a specific post-processing, the algorithm gives much more precise results on LFR benchmarks with high overlap compared to other algorithms and performs very similarly to GCE.

Path planning for persistent surveillance applications using fixed-wing unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Keller, James F.

This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles (UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission, fixed wing vehicles have maneuver constraints that can limit their performance in this role. Current technology vehicles are capable of long duration flight with a minimal acoustic footprint while carrying an array of cameras and sensors. Both military tactical and civilian safety applications can benefit from this technology. We make three main contributions: C1 A sequential path planner that generates a C 2 flight plan to persistently acquire a covering set of data over a user designated area of interest. The planner features the following innovations: • A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length. • A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction. • A smooth path generator that provides C 2 routes that satisfy user specified curvature constraints. C2 A set of algorithms to coordinate multiple UAVs, including mission commencement from arbitrary locations to the start of a coordinated mission and de-confliction of paths to avoid collisions with other vehicles and fixed obstacles. C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing validated through flight test experiments on multiple platforms. A variety of tests and platforms are discussed. The algorithms presented are based on a technical approach with approximately equal emphasis on analysis, computation, dynamic simulation, and flight test experimentation. Our planner (C1) directly takes into account vehicle maneuverability and agility constraints that could otherwise render simple solutions infeasible. This is especially important when surveillance objectives elevate the importance of optimized paths. Researchers have developed a diverse range of solutions for persistent surveillance applications but few directly address dynamic maneuver constraints. The key feature of C1 is a two stage sequential solution that discretizes the problem so that graph search techniques can be combined with parametric polynomial curve generation. A method to abstract the kino-dynamics of the aerial platforms is then presented so that a graph search solution can be adapted for this application. An A* Traveling Salesman Problem (TSP) algorithm is developed to search the discretized space using the abstract distance metric to acquire more data or avoid obstacles. Results of the graph search are then transcribed into smooth paths based on vehicle maneuver constraints. A complete solution for a single vehicle periodic tour of the area is developed using the results of the graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm (C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and to ensure there are no collisions at any of the path intersections. We present a toolbox of spline-based algorithms (C3) to streamline the development of C2 continuous paths with numerical stability. These tools are applied to an aerial persistent surveillance application to illustrate their utility. Comparisons with other parametric polynomial approaches are highlighted to underscore the benefits of the B-spline framework. Performance limits with respect to feasibility constraints are documented.

Three-dimensional choroidal segmentation in spectral OCT volumes using optic disc prior information

NASA Astrophysics Data System (ADS)

Hu, Zhihong; Girkin, Christopher A.; Hariri, Amirhossein; Sadda, SriniVas R.

2016-03-01

Recently, much attention has been focused on determining the role of the peripapillary choroid - the layer between the outer retinal pigment epithelium (RPE)/Bruchs membrane (BM) and choroid-sclera (C-S) junction, whether primary or secondary in the pathogenesis of glaucoma. However, the automated choroidal segmentation in spectral-domain optical coherence tomography (SD-OCT) images of optic nerve head (ONH) has not been reported probably due to the fact that the presence of the BM opening (BMO, corresponding to the optic disc) can deflect the choroidal segmentation from its correct position. The purpose of this study is to develop a 3D graph-based approach to identify the 3D choroidal layer in ONH-centered SD-OCT images using the BMO prior information. More specifically, an initial 3D choroidal segmentation was first performed using the 3D graph search algorithm. Note that varying surface interaction constraints based on the choroidal morphological model were applied. To assist the choroidal segmentation, two other surfaces of internal limiting membrane and innerouter segment junction were also segmented. Based on the segmented layer between the RPE/BM and C-S junction, a 2D projection map was created. The BMO in the projection map was detected by a 2D graph search. The pre-defined BMO information was then incorporated into the surface interaction constraints of the 3D graph search to obtain more accurate choroidal segmentation. Twenty SD-OCT images from 20 healthy subjects were used. The mean differences of the choroidal borders between the algorithm and manual segmentation were at a sub-voxel level, indicating a high level segmentation accuracy.

Approximation algorithms for the min-power symmetric connectivity problem

NASA Astrophysics Data System (ADS)

Plotnikov, Roman; Erzin, Adil; Mladenovic, Nenad

2016-10-01

We consider the NP-hard problem of synthesis of optimal spanning communication subgraph in a given arbitrary simple edge-weighted graph. This problem occurs in the wireless networks while minimizing the total transmission power consumptions. We propose several new heuristics based on the variable neighborhood search metaheuristic for the approximation solution of the problem. We have performed a numerical experiment where all proposed algorithms have been executed on the randomly generated test samples. For these instances, on average, our algorithms outperform the previously known heuristics.

SOI layout decomposition for double patterning lithography on high-performance computer platforms

NASA Astrophysics Data System (ADS)

Verstov, Vladimir; Zinchenko, Lyudmila; Makarchuk, Vladimir

2014-12-01

In the paper silicon on insulator layout decomposition algorithms for the double patterning lithography on high performance computing platforms are discussed. Our approach is based on the use of a contradiction graph and a modified concurrent breadth-first search algorithm. We evaluate our technique on 45 nm Nangate Open Cell Library including non-Manhattan geometry. Experimental results show that our soft computing algorithms decompose layout successfully and a minimal distance between polygons in layout is increased.

Private algorithms for the protected in social network search

PubMed Central

Kearns, Michael; Roth, Aaron; Wu, Zhiwei Steven; Yaroslavtsev, Grigory

2016-01-01

Motivated by tensions between data privacy for individual citizens and societal priorities such as counterterrorism and the containment of infectious disease, we introduce a computational model that distinguishes between parties for whom privacy is explicitly protected, and those for whom it is not (the targeted subpopulation). The goal is the development of algorithms that can effectively identify and take action upon members of the targeted subpopulation in a way that minimally compromises the privacy of the protected, while simultaneously limiting the expense of distinguishing members of the two groups via costly mechanisms such as surveillance, background checks, or medical testing. Within this framework, we provide provably privacy-preserving algorithms for targeted search in social networks. These algorithms are natural variants of common graph search methods, and ensure privacy for the protected by the careful injection of noise in the prioritization of potential targets. We validate the utility of our algorithms with extensive computational experiments on two large-scale social network datasets. PMID:26755606

Private algorithms for the protected in social network search.

PubMed

Kearns, Michael; Roth, Aaron; Wu, Zhiwei Steven; Yaroslavtsev, Grigory

2016-01-26

Motivated by tensions between data privacy for individual citizens and societal priorities such as counterterrorism and the containment of infectious disease, we introduce a computational model that distinguishes between parties for whom privacy is explicitly protected, and those for whom it is not (the targeted subpopulation). The goal is the development of algorithms that can effectively identify and take action upon members of the targeted subpopulation in a way that minimally compromises the privacy of the protected, while simultaneously limiting the expense of distinguishing members of the two groups via costly mechanisms such as surveillance, background checks, or medical testing. Within this framework, we provide provably privacy-preserving algorithms for targeted search in social networks. These algorithms are natural variants of common graph search methods, and ensure privacy for the protected by the careful injection of noise in the prioritization of potential targets. We validate the utility of our algorithms with extensive computational experiments on two large-scale social network datasets.

An annealed chaotic maximum neural network for bipartite subgraph problem.

PubMed

Wang, Jiahai; Tang, Zheng; Wang, Ronglong

2004-04-01

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.

Query-Adaptive Reciprocal Hash Tables for Nearest Neighbor Search.

PubMed

Liu, Xianglong; Deng, Cheng; Lang, Bo; Tao, Dacheng; Li, Xuelong

2016-02-01

Recent years have witnessed the success of binary hashing techniques in approximate nearest neighbor search. In practice, multiple hash tables are usually built using hashing to cover more desired results in the hit buckets of each table. However, rare work studies the unified approach to constructing multiple informative hash tables using any type of hashing algorithms. Meanwhile, for multiple table search, it also lacks of a generic query-adaptive and fine-grained ranking scheme that can alleviate the binary quantization loss suffered in the standard hashing techniques. To solve the above problems, in this paper, we first regard the table construction as a selection problem over a set of candidate hash functions. With the graph representation of the function set, we propose an efficient solution that sequentially applies normalized dominant set to finding the most informative and independent hash functions for each table. To further reduce the redundancy between tables, we explore the reciprocal hash tables in a boosting manner, where the hash function graph is updated with high weights emphasized on the misclassified neighbor pairs of previous hash tables. To refine the ranking of the retrieved buckets within a certain Hamming radius from the query, we propose a query-adaptive bitwise weighting scheme to enable fine-grained bucket ranking in each hash table, exploiting the discriminative power of its hash functions and their complement for nearest neighbor search. Moreover, we integrate such scheme into the multiple table search using a fast, yet reciprocal table lookup algorithm within the adaptive weighted Hamming radius. In this paper, both the construction method and the query-adaptive search method are general and compatible with different types of hashing algorithms using different feature spaces and/or parameter settings. Our extensive experiments on several large-scale benchmarks demonstrate that the proposed techniques can significantly outperform both the naive construction methods and the state-of-the-art hashing algorithms.

F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly.

PubMed

Jain, Swati; Schlick, Tamar

2017-11-24

Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications. Copyright © 2017 Elsevier Ltd. All rights reserved.

G-Bean: an ontology-graph based web tool for biomedical literature retrieval

PubMed Central

2014-01-01

Background Currently, most people use NCBI's PubMed to search the MEDLINE database, an important bibliographical information source for life science and biomedical information. However, PubMed has some drawbacks that make it difficult to find relevant publications pertaining to users' individual intentions, especially for non-expert users. To ameliorate the disadvantages of PubMed, we developed G-Bean, a graph based biomedical search engine, to search biomedical articles in MEDLINE database more efficiently. Methods G-Bean addresses PubMed's limitations with three innovations: (1) Parallel document index creation: a multithreaded index creation strategy is employed to generate the document index for G-Bean in parallel; (2) Ontology-graph based query expansion: an ontology graph is constructed by merging four major UMLS (Version 2013AA) vocabularies, MeSH, SNOMEDCT, CSP and AOD, to cover all concepts in National Library of Medicine (NLM) database; a Personalized PageRank algorithm is used to compute concept relevance in this ontology graph and the Term Frequency - Inverse Document Frequency (TF-IDF) weighting scheme is used to re-rank the concepts. The top 500 ranked concepts are selected for expanding the initial query to retrieve more accurate and relevant information; (3) Retrieval and re-ranking of documents based on user's search intention: after the user selects any article from the existing search results, G-Bean analyzes user's selections to determine his/her true search intention and then uses more relevant and more specific terms to retrieve additional related articles. The new articles are presented to the user in the order of their relevance to the already selected articles. Results Performance evaluation with 106 OHSUMED benchmark queries shows that G-Bean returns more relevant results than PubMed does when using these queries to search the MEDLINE database. PubMed could not even return any search result for some OHSUMED queries because it failed to form the appropriate Boolean query statement automatically from the natural language query strings. G-Bean is available at http://bioinformatics.clemson.edu/G-Bean/index.php. Conclusions G-Bean addresses PubMed's limitations with ontology-graph based query expansion, automatic document indexing, and user search intention discovery. It shows significant advantages in finding relevant articles from the MEDLINE database to meet the information need of the user. PMID:25474588

G-Bean: an ontology-graph based web tool for biomedical literature retrieval.

PubMed

Wang, James Z; Zhang, Yuanyuan; Dong, Liang; Li, Lin; Srimani, Pradip K; Yu, Philip S

2014-01-01

Currently, most people use NCBI's PubMed to search the MEDLINE database, an important bibliographical information source for life science and biomedical information. However, PubMed has some drawbacks that make it difficult to find relevant publications pertaining to users' individual intentions, especially for non-expert users. To ameliorate the disadvantages of PubMed, we developed G-Bean, a graph based biomedical search engine, to search biomedical articles in MEDLINE database more efficiently. G-Bean addresses PubMed's limitations with three innovations: (1) Parallel document index creation: a multithreaded index creation strategy is employed to generate the document index for G-Bean in parallel; (2) Ontology-graph based query expansion: an ontology graph is constructed by merging four major UMLS (Version 2013AA) vocabularies, MeSH, SNOMEDCT, CSP and AOD, to cover all concepts in National Library of Medicine (NLM) database; a Personalized PageRank algorithm is used to compute concept relevance in this ontology graph and the Term Frequency - Inverse Document Frequency (TF-IDF) weighting scheme is used to re-rank the concepts. The top 500 ranked concepts are selected for expanding the initial query to retrieve more accurate and relevant information; (3) Retrieval and re-ranking of documents based on user's search intention: after the user selects any article from the existing search results, G-Bean analyzes user's selections to determine his/her true search intention and then uses more relevant and more specific terms to retrieve additional related articles. The new articles are presented to the user in the order of their relevance to the already selected articles. Performance evaluation with 106 OHSUMED benchmark queries shows that G-Bean returns more relevant results than PubMed does when using these queries to search the MEDLINE database. PubMed could not even return any search result for some OHSUMED queries because it failed to form the appropriate Boolean query statement automatically from the natural language query strings. G-Bean is available at http://bioinformatics.clemson.edu/G-Bean/index.php. G-Bean addresses PubMed's limitations with ontology-graph based query expansion, automatic document indexing, and user search intention discovery. It shows significant advantages in finding relevant articles from the MEDLINE database to meet the information need of the user.

Using a Card Trick to Teach Discrete Mathematics

ERIC Educational Resources Information Center

Simonson, Shai; Holm, Tara S.

2003-01-01

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Ranking Information in Networks

NASA Astrophysics Data System (ADS)

Eliassi-Rad, Tina; Henderson, Keith

Given a network, we are interested in ranking sets of nodes that score highest on user-specified criteria. For instance in graphs from bibliographic data (e.g. PubMed), we would like to discover sets of authors with expertise in a wide range of disciplines. We present this ranking task as a Top-K problem; utilize fixed-memory heuristic search; and present performance of both the serial and distributed search algorithms on synthetic and real-world data sets.

Uncovering the overlapping community structure of complex networks by maximal cliques

NASA Astrophysics Data System (ADS)

Li, Junqiu; Wang, Xingyuan; Cui, Yaozu

2014-12-01

In this paper, a unique algorithm is proposed to detect overlapping communities in the un-weighted and weighted networks with considerable accuracy. The maximal cliques, overlapping vertex, bridge vertex and isolated vertex are introduced. First, all the maximal cliques are extracted by the algorithm based on the deep and bread searching. Then two maximal cliques can be merged into a larger sub-graph by some given rules. In addition, the proposed algorithm successfully finds overlapping vertices and bridge vertices between communities. Experimental results using some real-world networks data show that the performance of the proposed algorithm is satisfactory.

On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types

PubMed Central

2014-01-01

Background Integrating and analyzing heterogeneous genome-scale data is a huge algorithmic challenge for modern systems biology. Bipartite graphs can be useful for representing relationships across pairs of disparate data types, with the interpretation of these relationships accomplished through an enumeration of maximal bicliques. Most previously-known techniques are generally ill-suited to this foundational task, because they are relatively inefficient and without effective scaling. In this paper, a powerful new algorithm is described that produces all maximal bicliques in a bipartite graph. Unlike most previous approaches, the new method neither places undue restrictions on its input nor inflates the problem size. Efficiency is achieved through an innovative exploitation of bipartite graph structure, and through computational reductions that rapidly eliminate non-maximal candidates from the search space. An iterative selection of vertices for consideration based on non-decreasing common neighborhood sizes boosts efficiency and leads to more balanced recursion trees. Results The new technique is implemented and compared to previously published approaches from graph theory and data mining. Formal time and space bounds are derived. Experiments are performed on both random graphs and graphs constructed from functional genomics data. It is shown that the new method substantially outperforms the best previous alternatives. Conclusions The new method is streamlined, efficient, and particularly well-suited to the study of huge and diverse biological data. A robust implementation has been incorporated into GeneWeaver, an online tool for integrating and analyzing functional genomics experiments, available at http://geneweaver.org. The enormous increase in scalability it provides empowers users to study complex and previously unassailable gene-set associations between genes and their biological functions in a hierarchical fashion and on a genome-wide scale. This practical computational resource is adaptable to almost any applications environment in which bipartite graphs can be used to model relationships between pairs of heterogeneous entities. PMID:24731198

Finding Minimum-Power Broadcast Trees for Wireless Networks

NASA Technical Reports Server (NTRS)

Arabshahi, Payman; Gray, Andrew; Das, Arindam; El-Sharkawi, Mohamed; Marks, Robert, II

2004-01-01

Some algorithms have been devised for use in a method of constructing tree graphs that represent connections among the nodes of a wireless communication network. These algorithms provide for determining the viability of any given candidate connection tree and for generating an initial set of viable trees that can be used in any of a variety of search algorithms (e.g., a genetic algorithm) to find a tree that enables the network to broadcast from a source node to all other nodes while consuming the minimum amount of total power. The method yields solutions better than those of a prior algorithm known as the broadcast incremental power algorithm, albeit at a slightly greater computational cost.

Multilabel user classification using the community structure of online networks

PubMed Central

Papadopoulos, Symeon; Kompatsiaris, Yiannis

2017-01-01

We study the problem of semi-supervised, multi-label user classification of networked data in the online social platform setting. We propose a framework that combines unsupervised community extraction and supervised, community-based feature weighting before training a classifier. We introduce Approximate Regularized Commute-Time Embedding (ARCTE), an algorithm that projects the users of a social graph onto a latent space, but instead of packing the global structure into a matrix of predefined rank, as many spectral and neural representation learning methods do, it extracts local communities for all users in the graph in order to learn a sparse embedding. To this end, we employ an improvement of personalized PageRank algorithms for searching locally in each user’s graph structure. Then, we perform supervised community feature weighting in order to boost the importance of highly predictive communities. We assess our method performance on the problem of user classification by performing an extensive comparative study among various recent methods based on graph embeddings. The comparison shows that ARCTE significantly outperforms the competition in almost all cases, achieving up to 35% relative improvement compared to the second best competing method in terms of F1-score. PMID:28278242

Multilabel user classification using the community structure of online networks.

PubMed

Rizos, Georgios; Papadopoulos, Symeon; Kompatsiaris, Yiannis

2017-01-01

We study the problem of semi-supervised, multi-label user classification of networked data in the online social platform setting. We propose a framework that combines unsupervised community extraction and supervised, community-based feature weighting before training a classifier. We introduce Approximate Regularized Commute-Time Embedding (ARCTE), an algorithm that projects the users of a social graph onto a latent space, but instead of packing the global structure into a matrix of predefined rank, as many spectral and neural representation learning methods do, it extracts local communities for all users in the graph in order to learn a sparse embedding. To this end, we employ an improvement of personalized PageRank algorithms for searching locally in each user's graph structure. Then, we perform supervised community feature weighting in order to boost the importance of highly predictive communities. We assess our method performance on the problem of user classification by performing an extensive comparative study among various recent methods based on graph embeddings. The comparison shows that ARCTE significantly outperforms the competition in almost all cases, achieving up to 35% relative improvement compared to the second best competing method in terms of F1-score.

Irreconcilable difference between quantum walks and adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Wong, Thomas G.; Meyer, David A.

2016-06-01

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.

Top-k similar graph matching using TraM in biological networks.

PubMed

Amin, Mohammad Shafkat; Finley, Russell L; Jamil, Hasan M

2012-01-01

Many emerging database applications entail sophisticated graph-based query manipulation, predominantly evident in large-scale scientific applications. To access the information embedded in graphs, efficient graph matching tools and algorithms have become of prime importance. Although the prohibitively expensive time complexity associated with exact subgraph isomorphism techniques has limited its efficacy in the application domain, approximate yet efficient graph matching techniques have received much attention due to their pragmatic applicability. Since public domain databases are noisy and incomplete in nature, inexact graph matching techniques have proven to be more promising in terms of inferring knowledge from numerous structural data repositories. In this paper, we propose a novel technique called TraM for approximate graph matching that off-loads a significant amount of its processing on to the database making the approach viable for large graphs. Moreover, the vector space embedding of the graphs and efficient filtration of the search space enables computation of approximate graph similarity at a throw-away cost. We annotate nodes of the query graphs by means of their global topological properties and compare them with neighborhood biased segments of the datagraph for proper matches. We have conducted experiments on several real data sets, and have demonstrated the effectiveness and efficiency of the proposed method

An improved hierarchical A * algorithm in the optimization of parking lots

NASA Astrophysics Data System (ADS)

Wang, Yong; Wu, Junjuan; Wang, Ying

2017-08-01

In the parking lot parking path optimization, the traditional evaluation index is the shortest distance as the best index and it does not consider the actual road conditions. Now, the introduction of a more practical evaluation index can not only simplify the hardware design of the boot system but also save the software overhead. Firstly, we establish the parking lot network graph RPCDV mathematical model and all nodes in the network is divided into two layers which were constructed using different evaluation function base on the improved hierarchical A * algorithm which improves the time optimal path search efficiency and search precision of the evaluation index. The final results show that for different sections of the program attribute parameter algorithm always faster the time to find the optimal path.

[A retrieval method of drug molecules based on graph collapsing].

PubMed

Qu, J W; Lv, X Q; Liu, Z M; Liao, Y; Sun, P H; Wang, B; Tang, Z

2018-04-18

To establish a compact and efficient hypergraph representation and a graph-similarity-based retrieval method of molecules to achieve effective and efficient medicine information retrieval. Chemical structural formula (CSF) was a primary search target as a unique and precise identifier for each compound at the molecular level in the research field of medicine information retrieval. To retrieve medicine information effectively and efficiently, a complete workflow of the graph-based CSF retrieval system was introduced. This system accepted the photos taken from smartphones and the sketches drawn on tablet personal computers as CSF inputs, and formalized the CSFs with the corresponding graphs. Then this paper proposed a compact and efficient hypergraph representation for molecules on the basis of analyzing factors that directly affected the efficiency of graph matching. According to the characteristics of CSFs, a hierarchical collapsing method combining graph isomorphism and frequent subgraph mining was adopted. There was yet a fundamental challenge, subgraph overlapping during the collapsing procedure, which hindered the method from establishing the correct compact hypergraph of an original CSF graph. Therefore, a graph-isomorphism-based algorithm was proposed to select dominant acyclic subgraphs on the basis of overlapping analysis. Finally, the spatial similarity among graphical CSFs was evaluated by multi-dimensional measures of similarity. To evaluate the performance of the proposed method, the proposed system was firstly compared with Wikipedia Chemical Structure Explorer (WCSE), the state-of-the-art system that allowed CSF similarity searching within Wikipedia molecules dataset, on retrieval accuracy. The system achieved higher values on mean average precision, discounted cumulative gain, rank-biased precision, and expected reciprocal rank than WCSE from the top-2 to the top-10 retrieved results. Specifically, the system achieved 10%, 1.41, 6.42%, and 1.32% higher than WCSE on these metrics for top-10 retrieval results, respectively. Moreover, several retrieval cases were presented to intuitively compare with WCSE. The results of the above comparative study demonstrated that the proposed method outperformed the existing method with regard to accuracy and effectiveness. This paper proposes a graph-similarity-based retrieval approach for medicine information. To obtain satisfactory retrieval results, an isomorphism-based algorithm is proposed for dominant subgraph selection based on the subgraph overlapping analysis, as well as an effective and efficient hypergraph representation of molecules. Experiment results demonstrate the effectiveness of the proposed approach.

A distributed algorithm to maintain and repair the trail networks of arboreal ants.

PubMed

Chandrasekhar, Arjun; Gordon, Deborah M; Navlakha, Saket

2018-06-18

We study how the arboreal turtle ant (Cephalotes goniodontus) solves a fundamental computing problem: maintaining a trail network and finding alternative paths to route around broken links in the network. Turtle ants form a routing backbone of foraging trails linking several nests and temporary food sources. This species travels only in the trees, so their foraging trails are constrained to lie on a natural graph formed by overlapping branches and vines in the tangled canopy. Links between branches, however, can be ephemeral, easily destroyed by wind, rain, or animal movements. Here we report a biologically feasible distributed algorithm, parameterized using field data, that can plausibly describe how turtle ants maintain the routing backbone and find alternative paths to circumvent broken links in the backbone. We validate the ability of this probabilistic algorithm to circumvent simulated breaks in synthetic and real-world networks, and we derive an analytic explanation for why certain features are crucial to improve the algorithm's success. Our proposed algorithm uses fewer computational resources than common distributed graph search algorithms, and thus may be useful in other domains, such as for swarm computing or for coordinating molecular robots.

Automatic segmentation of mitochondria in EM data using pairwise affinity factorization and graph-based contour searching.

PubMed

Ghita, Ovidiu; Dietlmeier, Julia; Whelan, Paul F

2014-10-01

In this paper, we investigate the segmentation of closed contours in subcellular data using a framework that primarily combines the pairwise affinity grouping principles with a graph partitioning contour searching approach. One salient problem that precluded the application of these methods to large scale segmentation problems is the onerous computational complexity required to generate comprehensive representations that include all pairwise relationships between all pixels in the input data. To compensate for this problem, a practical solution is to reduce the complexity of the input data by applying an over-segmentation technique prior to the application of the computationally demanding strands of the segmentation process. This approach opens the opportunity to build specific shape and intensity models that can be successfully employed to extract the salient structures in the input image which are further processed to identify the cycles in an undirected graph. The proposed framework has been applied to the segmentation of mitochondria membranes in electron microscopy data which are characterized by low contrast and low signal-to-noise ratio. The algorithm has been quantitatively evaluated using two datasets where the segmentation results have been compared with the corresponding manual annotations. The performance of the proposed algorithm has been measured using standard metrics, such as precision and recall, and the experimental results indicate a high level of segmentation accuracy.

Efficient Generation of Dancing Animation Synchronizing with Music Based on Meta Motion Graphs

NASA Astrophysics Data System (ADS)

Xu, Jianfeng; Takagi, Koichi; Sakazawa, Shigeyuki

This paper presents a system for automatic generation of dancing animation that is synchronized with a piece of music by re-using motion capture data. Basically, the dancing motion is synthesized according to the rhythm and intensity features of music. For this purpose, we propose a novel meta motion graph structure to embed the necessary features including both rhythm and intensity, which is constructed on the motion capture database beforehand. In this paper, we consider two scenarios for non-streaming music and streaming music, where global search and local search are required respectively. In the case of the former, once a piece of music is input, the efficient dynamic programming algorithm can be employed to globally search a best path in the meta motion graph, where an objective function is properly designed by measuring the quality of beat synchronization, intensity matching, and motion smoothness. In the case of the latter, the input music is stored in a buffer in a streaming mode, then an efficient search method is presented for a certain amount of music data (called a segment) in the buffer with the same objective function, resulting in a segment-based search approach. For streaming applications, we define an additional property in the above meta motion graph to deal with the unpredictable future music, which guarantees that there is some motion to match the unknown remaining music. A user study with totally 60 subjects demonstrates that our system outperforms the stat-of-the-art techniques in both scenarios. Furthermore, our system improves the synthesis speed greatly (maximal speedup is more than 500 times), which is essential for mobile applications. We have implemented our system on commercially available smart phones and confirmed that it works well on these mobile phones.

featsel: A framework for benchmarking of feature selection algorithms and cost functions

NASA Astrophysics Data System (ADS)

Reis, Marcelo S.; Estrela, Gustavo; Ferreira, Carlos Eduardo; Barrera, Junior

In this paper, we introduce featsel, a framework for benchmarking of feature selection algorithms and cost functions. This framework allows the user to deal with the search space as a Boolean lattice and has its core coded in C++ for computational efficiency purposes. Moreover, featsel includes Perl scripts to add new algorithms and/or cost functions, generate random instances, plot graphs and organize results into tables. Besides, this framework already comes with dozens of algorithms and cost functions for benchmarking experiments. We also provide illustrative examples, in which featsel outperforms the popular Weka workbench in feature selection procedures on data sets from the UCI Machine Learning Repository.

Pyramid algorithms as models of human cognition

NASA Astrophysics Data System (ADS)

Pizlo, Zygmunt; Li, Zheng

2003-06-01

There is growing body of experimental evidence showing that human perception and cognition involves mechanisms that can be adequately modeled by pyramid algorithms. The main aspect of those mechanisms is hierarchical clustering of information: visual images, spatial relations, and states as well as transformations of a problem. In this paper we review prior psychophysical and simulation results on visual size transformation, size discrimination, speed-accuracy tradeoff, figure-ground segregation, and the traveling salesman problem. We also present our new results on graph search and on the 15-puzzle.

Graph-Based Semantic Web Service Composition for Healthcare Data Integration.

PubMed

Arch-Int, Ngamnij; Arch-Int, Somjit; Sonsilphong, Suphachoke; Wanchai, Paweena

2017-01-01

Within the numerous and heterogeneous web services offered through different sources, automatic web services composition is the most convenient method for building complex business processes that permit invocation of multiple existing atomic services. The current solutions in functional web services composition lack autonomous queries of semantic matches within the parameters of web services, which are necessary in the composition of large-scale related services. In this paper, we propose a graph-based Semantic Web Services composition system consisting of two subsystems: management time and run time. The management-time subsystem is responsible for dependency graph preparation in which a dependency graph of related services is generated automatically according to the proposed semantic matchmaking rules. The run-time subsystem is responsible for discovering the potential web services and nonredundant web services composition of a user's query using a graph-based searching algorithm. The proposed approach was applied to healthcare data integration in different health organizations and was evaluated according to two aspects: execution time measurement and correctness measurement.

Graph-Based Semantic Web Service Composition for Healthcare Data Integration

PubMed Central

2017-01-01

Within the numerous and heterogeneous web services offered through different sources, automatic web services composition is the most convenient method for building complex business processes that permit invocation of multiple existing atomic services. The current solutions in functional web services composition lack autonomous queries of semantic matches within the parameters of web services, which are necessary in the composition of large-scale related services. In this paper, we propose a graph-based Semantic Web Services composition system consisting of two subsystems: management time and run time. The management-time subsystem is responsible for dependency graph preparation in which a dependency graph of related services is generated automatically according to the proposed semantic matchmaking rules. The run-time subsystem is responsible for discovering the potential web services and nonredundant web services composition of a user's query using a graph-based searching algorithm. The proposed approach was applied to healthcare data integration in different health organizations and was evaluated according to two aspects: execution time measurement and correctness measurement. PMID:29065602

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

DOE PAGES

Azad, Ariful; Buluç, Aydın

2016-05-16

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributed-memory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal matching algorithms with minimal changes. The newly developed algorithms have two benefits over existing graph-based algorithms. First, unlike existing parallel algorithms, cardinality of matching obtained by the new algorithms stays constant with increasing processor counts, which is important for predictable and reproducible performance. Second, relying on bulk-synchronous matrix operations,more » these algorithms expose a higher degree of parallelism on distributed-memory platforms than existing graph-based algorithms. We report high-performance implementations of three maximal matching algorithms using hybrid OpenMP-MPI and evaluate the performance of these algorithm using more than 35 real and randomly generated graphs. On real instances, our algorithms achieve up to 200 × speedup on 2048 cores of a Cray XC30 supercomputer. Even higher speedups are obtained on larger synthetically generated graphs where our algorithms show good scaling on up to 16,384 cores.« less

Graph-based normalization and whitening for non-linear data analysis.

PubMed

Aaron, Catherine

2006-01-01

In this paper we construct a graph-based normalization algorithm for non-linear data analysis. The principle of this algorithm is to get a spherical average neighborhood with unit radius. First we present a class of global dispersion measures used for "global normalization"; we then adapt these measures using a weighted graph to build a local normalization called "graph-based" normalization. Then we give details of the graph-based normalization algorithm and illustrate some results. In the second part we present a graph-based whitening algorithm built by analogy between the "global" and the "local" problem.

Exploring the full catalytic cycle of rhodium(i)–BINAP-catalysed isomerisation of allylic amines: a graph theory approach for path optimisation† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sc00401j Click here for additional data file.

PubMed Central

Yoshimura, Takayoshi; Taketsugu, Tetsuya; Sawamura, Masaya

2017-01-01

We explored the reaction mechanism of the cationic rhodium(i)–BINAP complex catalysed isomerisation of allylic amines using the artificial force induced reaction method with the global reaction route mapping strategy, which enabled us to search for various reaction paths without assumption of transition states. The entire reaction network was reproduced in the form of a graph, and reasonable paths were selected from the complicated network using Prim’s algorithm. As a result, a new dissociative reaction mechanism was proposed. Our comprehensive reaction path search provided rationales for the E/Z and S/R selectivities of the stereoselective reaction. PMID:28970877

Approximate matching of structured motifs in DNA sequences.

PubMed

El-Mabrouk, Nadia; Raffinot, Mathieu; Duchesne, Jean-Eudes; Lajoie, Mathieu; Luc, Nicolas

2005-04-01

Several methods have been developed for identifying more or less complex RNA structures in a genome. All these methods are based on the search for conserved primary and secondary sub-structures. In this paper, we present a simple formal representation of a helix, which is a combination of sequence and folding constraints, as a constrained regular expression. This representation allows us to develop a well-founded algorithm that searches for all approximate matches of a helix in a genome. The algorithm is based on an alignment graph constructed from several copies of a pushdown automaton, arranged one on top of another. This is a first attempt to take advantage of the possibilities of pushdown automata in the context of approximate matching. The worst time complexity is O(krpn), where k is the error threshold, n the size of the genome, p the size of the secondary expression, and r its number of union symbols. We then extend the algorithm to search for pseudo-knots and secondary structures containing an arbitrary number of helices.

Coined quantum walks on weighted graphs

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-11-01

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy’s quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover’s algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when l < 3 + 2\\sqrt{2} ≈ 5.828 .

Quantitative analysis of airway abnormalities in CT

NASA Astrophysics Data System (ADS)

Petersen, Jens; Lo, Pechin; Nielsen, Mads; Edula, Goutham; Ashraf, Haseem; Dirksen, Asger; de Bruijne, Marleen

2010-03-01

A coupled surface graph cut algorithm for airway wall segmentation from Computed Tomography (CT) images is presented. Using cost functions that highlight both inner and outer wall borders, the method combines the search for both borders into one graph cut. The proposed method is evaluated on 173 manually segmented images extracted from 15 different subjects and shown to give accurate results, with 37% less errors than the Full Width at Half Maximum (FWHM) algorithm and 62% less than a similar graph cut method without coupled surfaces. Common measures of airway wall thickness such as the Interior Area (IA) and Wall Area percentage (WA%) was measured by the proposed method on a total of 723 CT scans from a lung cancer screening study. These measures were significantly different for participants with Chronic Obstructive Pulmonary Disease (COPD) compared to asymptomatic participants. Furthermore, reproducibility was good as confirmed by repeat scans and the measures correlated well with the outcomes of pulmonary function tests, demonstrating the use of the algorithm as a COPD diagnostic tool. Additionally, a new measure of airway wall thickness is proposed, Normalized Wall Intensity Sum (NWIS). NWIS is shown to correlate better with lung function test values and to be more reproducible than previous measures IA, WA% and airway wall thickness at a lumen perimeter of 10 mm (PI10).

A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation.

PubMed

Wang, Zhaocai; Huang, Dongmei; Meng, Huajun; Tang, Chengpei

2013-10-01

The minimum spanning tree (MST) problem is to find minimum edge connected subsets containing all the vertex of a given undirected graph. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications. Moreover in previous studies, DNA molecular operations usually were used to solve NP-complete head-to-tail path search problems, rarely for NP-hard problems with multi-lateral path solutions result, such as the minimum spanning tree problem. In this paper, we present a new fast DNA algorithm for solving the MST problem using DNA molecular operations. For an undirected graph with n vertex and m edges, we reasonably design flexible length DNA strands representing the vertex and edges, take appropriate steps and get the solutions of the MST problem in proper length range and O(3m+n) time complexity. We extend the application of DNA molecular operations and simultaneity simplify the complexity of the computation. Results of computer simulative experiments show that the proposed method updates some of the best known values with very short time and that the proposed method provides a better performance with solution accuracy over existing algorithms. Copyright © 2013 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Graphing trillions of triangles.

PubMed

Burkhardt, Paul

2017-07-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

The Container Problem in Bubble-Sort Graphs

NASA Astrophysics Data System (ADS)

Suzuki, Yasuto; Kaneko, Keiichi

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

Graphs, matrices, and the GraphBLAS: Seven good reasons

DOE PAGES

Kepner, Jeremy; Bader, David; Buluç, Aydın; ...

2015-01-01

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implementmore » a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.« less

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

An O([Formula: see text]) algorithm for sorting signed genomes by reversals, transpositions, transreversals and block-interchanges.

PubMed

Yu, Shuzhi; Hao, Fanchang; Leong, Hon Wai

2016-02-01

We consider the problem of sorting signed permutations by reversals, transpositions, transreversals, and block-interchanges. The problem arises in the study of species evolution via large-scale genome rearrangement operations. Recently, Hao et al. gave a 2-approximation scheme called genome sorting by bridges (GSB) for solving this problem. Their result extended and unified the results of (i) He and Chen - a 2-approximation algorithm allowing reversals, transpositions, and block-interchanges (by also allowing transversals) and (ii) Hartman and Sharan - a 1.5-approximation algorithm allowing reversals, transpositions, and transversals (by also allowing block-interchanges). The GSB result is based on introduction of three bridge structures in the breakpoint graph, the L-bridge, T-bridge, and X-bridge that models goodreversal, transposition/transreversal, and block-interchange, respectively. However, the paper by Hao et al. focused on proving the 2-approximation GSB scheme and only mention a straightforward [Formula: see text] algorithm. In this paper, we give an [Formula: see text] algorithm for implementing the GSB scheme. The key idea behind our faster GSB algorithm is to represent cycles in the breakpoint graph by their canonical sequences, which greatly simplifies the search for these bridge structures. We also give some comparison results (running time and computed distances) against the original GSB implementation.

Algorithm of composing the schedule of construction and installation works

NASA Astrophysics Data System (ADS)

Nehaj, Rustam; Molotkov, Georgij; Rudchenko, Ivan; Grinev, Anatolij; Sekisov, Aleksandr

2017-10-01

An algorithm for scheduling works is developed, in which the priority of the work corresponds to the total weight of the subordinate works, the vertices of the graph, and it is proved that for graphs of the tree type the algorithm is optimal. An algorithm is synthesized to reduce the search for solutions when drawing up schedules of construction and installation works, allocating a subset with the optimal solution of the problem of the minimum power, which is determined by the structure of its initial data and numerical values. An algorithm for scheduling construction and installation work is developed, taking into account the schedule for the movement of brigades, which is characterized by the possibility to efficiently calculate the values of minimizing the time of work performance by the parameters of organizational and technological reliability through the use of the branch and boundary method. The program of the computational algorithm was compiled in the MatLAB-2008 program. For the initial data of the matrix, random numbers were taken, uniformly distributed in the range from 1 to 100. It takes 0.5; 2.5; 7.5; 27 minutes to solve the problem. Thus, the proposed method for estimating the lower boundary of the solution is sufficiently accurate and allows efficient solution of the minimax task of scheduling construction and installation works.

Survey of Approaches to Generate Realistic Synthetic Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Seung-Hwan; Lee, Sangkeun; Powers, Sarah S

A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broadmore » set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.« less

Searches over graphs representing geospatial-temporal remote sensing data

DOEpatents

Brost, Randolph; Perkins, David Nikolaus

2018-03-06

Various technologies pertaining to identifying objects of interest in remote sensing images by searching over geospatial-temporal graph representations are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Geospatial-temporal graph searches are made computationally efficient by taking advantage of characteristics of geospatial-temporal data in remote sensing images through the application of various graph search techniques.

Weights and topology: a study of the effects of graph construction on 3D image segmentation.

PubMed

Grady, Leo; Jolly, Marie-Pierre

2008-01-01

Graph-based algorithms have become increasingly popular for medical image segmentation. The fundamental process for each of these algorithms is to use the image content to generate a set of weights for the graph and then set conditions for an optimal partition of the graph with respect to these weights. To date, the heuristics used for generating the weighted graphs from image intensities have largely been ignored, while the primary focus of attention has been on the details of providing the partitioning conditions. In this paper we empirically study the effects of graph connectivity and weighting function on the quality of the segmentation results. To control for algorithm-specific effects, we employ both the Graph Cuts and Random Walker algorithms in our experiments.

Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.

PubMed

Kundeti, Vamsi K; Rajasekaran, Sanguthevar; Dinh, Hieu; Vaughn, Matthew; Thapar, Vishal

2010-11-15

Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories - based on the data structures which they employ. The first class uses an overlap/string graph and the second type uses a de Bruijn graph. However with the recent advances in short read sequencing technology, de Bruijn graph based algorithms seem to play a vital role in practice. Efficient algorithms for building these massive de Bruijn graphs are very essential in large sequencing projects based on short reads. In an earlier work, an O(n/p) time parallel algorithm has been given for this problem. Here n is the size of the input and p is the number of processors. This algorithm enumerates all possible bi-directed edges which can overlap with a node and ends up generating Θ(nΣ) messages (Σ being the size of the alphabet). In this paper we present a Θ(n/p) time parallel algorithm with a communication complexity that is equal to that of parallel sorting and is not sensitive to Σ. The generality of our algorithm makes it very easy to extend it even to the out-of-core model and in this case it has an optimal I/O complexity of Θ(nlog(n/B)Blog(M/B)) (M being the main memory size and B being the size of the disk block). We demonstrate the scalability of our parallel algorithm on a SGI/Altix computer. A comparison of our algorithm with the previous approaches reveals that our algorithm is faster--both asymptotically and practically. We demonstrate the scalability of our sequential out-of-core algorithm by comparing it with the algorithm used by VELVET to build the bi-directed de Bruijn graph. Our experiments reveal that our algorithm can build the graph with a constant amount of memory, which clearly outperforms VELVET. We also provide efficient algorithms for the bi-directed chain compaction problem. The bi-directed de Bruijn graph is a fundamental data structure for any sequence assembly program based on Eulerian approach. Our algorithms for constructing Bi-directed de Bruijn graphs are efficient in parallel and out of core settings. These algorithms can be used in building large scale bi-directed de Bruijn graphs. Furthermore, our algorithms do not employ any all-to-all communications in a parallel setting and perform better than the prior algorithms. Finally our out-of-core algorithm is extremely memory efficient and can replace the existing graph construction algorithm in VELVET.

JavaGenes: Evolving Graphs with Crossover

NASA Technical Reports Server (NTRS)

Globus, Al; Atsatt, Sean; Lawton, John; Wipke, Todd

2000-01-01

Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.

Graphing trillions of triangles

PubMed Central

Burkhardt, Paul

2016-01-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed. PMID:28690426

Shared-hole graph search with adaptive constraints for 3D optic nerve head optical coherence tomography image segmentation

PubMed Central

Yu, Kai; Shi, Fei; Gao, Enting; Zhu, Weifang; Chen, Haoyu; Chen, Xinjian

2018-01-01

Optic nerve head (ONH) is a crucial region for glaucoma detection and tracking based on spectral domain optical coherence tomography (SD-OCT) images. In this region, the existence of a “hole” structure makes retinal layer segmentation and analysis very challenging. To improve retinal layer segmentation, we propose a 3D method for ONH centered SD-OCT image segmentation, which is based on a modified graph search algorithm with a shared-hole and locally adaptive constraints. With the proposed method, both the optic disc boundary and nine retinal surfaces can be accurately segmented in SD-OCT images. An overall mean unsigned border positioning error of 7.27 ± 5.40 µm was achieved for layer segmentation, and a mean Dice coefficient of 0.925 ± 0.03 was achieved for optic disc region detection. PMID:29541497

Topological properties of the limited penetrable horizontal visibility graph family

NASA Astrophysics Data System (ADS)

Wang, Minggang; Vilela, André L. M.; Du, Ruijin; Zhao, Longfeng; Dong, Gaogao; Tian, Lixin; Stanley, H. Eugene

2018-05-01

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.

Dynamic graph cuts for efficient inference in Markov Random Fields.

PubMed

Kohli, Pushmeet; Torr, Philip H S

2007-12-01

Abstract-In this paper we present a fast new fully dynamic algorithm for the st-mincut/max-flow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of the max-flow problem on a graph, the dynamic algorithm efficiently computes the maximum flow in a modified version of the graph. The time taken by it is roughly proportional to the total amount of change in the edge weights of the graph. Our experiments show that, when the number of changes in the graph is small, the dynamic algorithm is significantly faster than the best known static graph cut algorithm. We test the performance of our algorithm on one particular problem: the object-background segmentation problem for video. It should be noted that the application of our algorithm is not limited to the above problem, the algorithm is generic and can be used to yield similar improvements in many other cases that involve dynamic change.

G-Hash: Towards Fast Kernel-based Similarity Search in Large Graph Databases.

PubMed

Wang, Xiaohong; Smalter, Aaron; Huan, Jun; Lushington, Gerald H

2009-01-01

Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others.Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models for supervised learning, graph kernel functions have (i) high computational complexity and (ii) non-trivial difficulty to be indexed in a graph database.Our objective is to bridge graph kernel function and similarity search in graph databases by proposing (i) a novel kernel-based similarity measurement and (ii) an efficient indexing structure for graph data management. Our method of similarity measurement builds upon local features extracted from each node and their neighboring nodes in graphs. A hash table is utilized to support efficient storage and fast search of the extracted local features. Using the hash table, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing. We have implemented our method, which we have named G-hash, and have demonstrated its utility on large chemical graph databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Most importantly, the new similarity measurement and the index structure is scalable to large database with smaller indexing size, faster indexing construction time, and faster query processing time as compared to state-of-the-art indexing methods such as C-tree, gIndex, and GraphGrep.

Graph drawing using tabu search coupled with path relinking.

PubMed

Dib, Fadi K; Rodgers, Peter

2018-01-01

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function's value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.

Graph drawing using tabu search coupled with path relinking

PubMed Central

Rodgers, Peter

2018-01-01

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function’s value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset. PMID:29746576

On the Effect of Group Structures on Ranking Strategies in Folksonomies

NASA Astrophysics Data System (ADS)

Abel, Fabian; Henze, Nicola; Krause, Daniel; Kriesell, Matthias

Folksonomies have shown interesting potential for improving information discovery and exploration. Recent folksonomy systems explore the use of tag assignments, which combine Web resources with annotations (tags), and the users that have created the annotations. This article investigates on the effect of grouping resources in folksonomies, i.e. creating sets of resources, and using this additional structure for the tasks of search & ranking, and for tag recommendations. We propose several group-sensitive extensions of graph-based search and recommendation algorithms, and compare them with non group-sensitive versions. Our experiments show that the quality of search result ranking can be significantly improved by introducing and exploiting the grouping of resources (one-tailed t-Test, level of significance α=0.05). Furthermore, tag recommendations profit from the group context, and it is possible to make very good recommendations even for untagged resources- which currently known tag recommendation algorithms cannot fulfill.

An Adiabatic Quantum Algorithm for Determining Gracefulness of a Graph

NASA Astrophysics Data System (ADS)

Hosseini, Sayed Mohammad; Davoudi Darareh, Mahdi; Janbaz, Shahrooz; Zaghian, Ali

2017-07-01

Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph G with e edges, is to label the vertices of G with 0, 1, ℒ, e such that, if we specify to each edge the difference value between its two ends, then any of 1, 2, ℒ, e appears exactly once as an edge label. For a given graph, there are still few efficient classical algorithms that determine either it is graceful or not, even for trees - as a well-known class of graphs. In this paper, we introduce an adiabatic quantum algorithm, which for a graceful graph G finds a graceful labelling. Also, this algorithm can determine if G is not graceful. Numerical simulations of the algorithm reveal that its time complexity has a polynomial behaviour with the problem size up to the range of 15 qubits. A general sufficient condition for a combinatorial optimization problem to have a satisfying adiabatic solution is also derived.

Enforced Sparse Non-Negative Matrix Factorization

DTIC Science & Technology

2016-01-23

documents to find interesting pieces of information. With limited resources, analysts often employ automated text - mining tools that highlight common...represented as an undirected bipartite graph. It has become a common method for generating topic models of text data because it is known to produce good results...model and the convergence rate of the underlying algorithm. I. Introduction A common analyst challenge is searching through large quantities of text

Graph Databases for Large-Scale Healthcare Systems: A Framework for Efficient Data Management and Data Services

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Yubin; Shankar, Mallikarjun; Park, Byung H.

Designing a database system for both efficient data management and data services has been one of the enduring challenges in the healthcare domain. In many healthcare systems, data services and data management are often viewed as two orthogonal tasks; data services refer to retrieval and analytic queries such as search, joins, statistical data extraction, and simple data mining algorithms, while data management refers to building error-tolerant and non-redundant database systems. The gap between service and management has resulted in rigid database systems and schemas that do not support effective analytics. We compose a rich graph structure from an abstracted healthcaremore » RDBMS to illustrate how we can fill this gap in practice. We show how a healthcare graph can be automatically constructed from a normalized relational database using the proposed 3NF Equivalent Graph (3EG) transformation.We discuss a set of real world graph queries such as finding self-referrals, shared providers, and collaborative filtering, and evaluate their performance over a relational database and its 3EG-transformed graph. Experimental results show that the graph representation serves as multiple de-normalized tables, thus reducing complexity in a database and enhancing data accessibility of users. Based on this finding, we propose an ensemble framework of databases for healthcare applications.« less

A Linear Kernel for Co-Path/Cycle Packing

NASA Astrophysics Data System (ADS)

Chen, Zhi-Zhong; Fellows, Michael; Fu, Bin; Jiang, Haitao; Liu, Yang; Wang, Lusheng; Zhu, Binhai

Bounded-Degree Vertex Deletion is a fundamental problem in graph theory that has new applications in computational biology. In this paper, we address a special case of Bounded-Degree Vertex Deletion, the Co-Path/Cycle Packing problem, which asks to delete as few vertices as possible such that the graph of the remaining (residual) vertices is composed of disjoint paths and simple cycles. The problem falls into the well-known class of 'node-deletion problems with hereditary properties', is hence NP-complete and unlikely to admit a polynomial time approximation algorithm with approximation factor smaller than 2. In the framework of parameterized complexity, we present a kernelization algorithm that produces a kernel with at most 37k vertices, improving on the super-linear kernel of Fellows et al.'s general theorem for Bounded-Degree Vertex Deletion. Using this kernel,and the method of bounded search trees, we devise an FPT algorithm that runs in time O *(3.24 k ). On the negative side, we show that the problem is APX-hard and unlikely to have a kernel smaller than 2k by a reduction from Vertex Cover.

Planning the FUSE Mission Using the SOVA Algorithm

NASA Technical Reports Server (NTRS)

Lanzi, James; Heatwole, Scott; Ward, Philip R.; Civeit, Thomas; Calvani, Humberto; Kruk, Jeffrey W.; Suchkov, Anatoly

2011-01-01

Three documents discuss the Sustainable Objective Valuation and Attainability (SOVA) algorithm and software as used to plan tasks (principally, scientific observations and associated maneuvers) for the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite. SOVA is a means of managing risk in a complex system, based on a concept of computing the expected return value of a candidate ordered set of tasks as a product of pre-assigned task values and assessments of attainability made against qualitatively defined strategic objectives. For the FUSE mission, SOVA autonomously assembles a week-long schedule of target observations and associated maneuvers so as to maximize the expected scientific return value while keeping the satellite stable, managing the angular momentum of spacecraft attitude- control reaction wheels, and striving for other strategic objectives. A six-degree-of-freedom model of the spacecraft is used in simulating the tasks, and the attainability of a task is calculated at each step by use of strategic objectives as defined by use of fuzzy inference systems. SOVA utilizes a variant of a graph-search algorithm known as the A* search algorithm to assemble the tasks into a week-long target schedule, using the expected scientific return value to guide the search.

Graph embedding and extensions: a general framework for dimensionality reduction.

PubMed

Yan, Shuicheng; Xu, Dong; Zhang, Benyu; Zhang, Hong-Jiang; Yang, Qiang; Lin, Stephen

2007-01-01

Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

PageRank without hyperlinks: Reranking with PubMed related article networks for biomedical text retrieval

PubMed Central

Lin, Jimmy

2008-01-01

Background Graph analysis algorithms such as PageRank and HITS have been successful in Web environments because they are able to extract important inter-document relationships from manually-created hyperlinks. We consider the application of these techniques to biomedical text retrieval. In the current PubMed® search interface, a MEDLINE® citation is connected to a number of related citations, which are in turn connected to other citations. Thus, a MEDLINE record represents a node in a vast content-similarity network. This article explores the hypothesis that these networks can be exploited for text retrieval, in the same manner as hyperlink graphs on the Web. Results We conducted a number of reranking experiments using the TREC 2005 genomics track test collection in which scores extracted from PageRank and HITS analysis were combined with scores returned by an off-the-shelf retrieval engine. Experiments demonstrate that incorporating PageRank scores yields significant improvements in terms of standard ranked-retrieval metrics. Conclusion The link structure of content-similarity networks can be exploited to improve the effectiveness of information retrieval systems. These results generalize the applicability of graph analysis algorithms to text retrieval in the biomedical domain. PMID:18538027

Modification of Prim’s algorithm on complete broadcasting graph

NASA Astrophysics Data System (ADS)

Dairina; Arif, Salmawaty; Munzir, Said; Halfiani, Vera; Ramli, Marwan

2017-09-01

Broadcasting is an information dissemination from one object to another object through communication between two objects in a network. Broadcasting for n objects can be solved by n - 1 communications and minimum time unit defined by ⌈2log n⌉ In this paper, weighted graph broadcasting is considered. The minimum weight of a complete broadcasting graph will be determined. Broadcasting graph is said to be complete if every vertex is connected. Thus to determine the minimum weight of complete broadcasting graph is equivalent to determine the minimum spanning tree of a complete graph. The Kruskal’s and Prim’s algorithm will be used to determine the minimum weight of a complete broadcasting graph regardless the minimum time unit ⌈2log n⌉ and modified Prim’s algorithm for the problems of the minimum time unit ⌈2log n⌉ is done. As an example case, here, the training of trainer problem is solved using these algorithms.

On a programming language for graph algorithms

NASA Technical Reports Server (NTRS)

Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.

1971-01-01

An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.

FGRAAL: FORTRAN extended graph algorithmic language

NASA Technical Reports Server (NTRS)

Basili, V. R.; Mesztenyi, C. K.; Rheinboldt, W. C.

1972-01-01

The FORTRAN version FGRAAL of the graph algorithmic language GRAAL as it has been implemented for the Univac 1108 is described. FBRAAL is an extension of FORTRAN 5 and is intended for describing and implementing graph algorithms of the type primarily arising in applications. The formal description contained in this report represents a supplement to the FORTRAN 5 manual for the Univac 1108 (UP-4060), that is, only the new features of the language are described. Several typical graph algorithms, written in FGRAAL, are included to illustrate various features of the language and to show its applicability.

Automatic extraction of protein point mutations using a graph bigram association.

PubMed

Lee, Lawrence C; Horn, Florence; Cohen, Fred E

2007-02-02

Protein point mutations are an essential component of the evolutionary and experimental analysis of protein structure and function. While many manually curated databases attempt to index point mutations, most experimentally generated point mutations and the biological impacts of the changes are described in the peer-reviewed published literature. We describe an application, Mutation GraB (Graph Bigram), that identifies, extracts, and verifies point mutations from biomedical literature. The principal problem of point mutation extraction is to link the point mutation with its associated protein and organism of origin. Our algorithm uses a graph-based bigram traversal to identify these relevant associations and exploits the Swiss-Prot protein database to verify this information. The graph bigram method is different from other models for point mutation extraction in that it incorporates frequency and positional data of all terms in an article to drive the point mutation-protein association. Our method was tested on 589 articles describing point mutations from the G protein-coupled receptor (GPCR), tyrosine kinase, and ion channel protein families. We evaluated our graph bigram metric against a word-proximity metric for term association on datasets of full-text literature in these three different protein families. Our testing shows that the graph bigram metric achieves a higher F-measure for the GPCRs (0.79 versus 0.76), protein tyrosine kinases (0.72 versus 0.69), and ion channel transporters (0.76 versus 0.74). Importantly, in situations where more than one protein can be assigned to a point mutation and disambiguation is required, the graph bigram metric achieves a precision of 0.84 compared with the word distance metric precision of 0.73. We believe the graph bigram search metric to be a significant improvement over previous search metrics for point mutation extraction and to be applicable to text-mining application requiring the association of words.

A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree.

PubMed

Nagoor Gani, A; Latha, S R

2016-01-01

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.

Weighted graph cuts without eigenvectors a multilevel approach.

PubMed

Dhillon, Inderjit S; Guan, Yuqiang; Kulis, Brian

2007-11-01

A variety of clustering algorithms have recently been proposed to handle data that is not linearly separable; spectral clustering and kernel k-means are two of the main methods. In this paper, we discuss an equivalence between the objective functions used in these seemingly different methods--in particular, a general weighted kernel k-means objective is mathematically equivalent to a weighted graph clustering objective. We exploit this equivalence to develop a fast, high-quality multilevel algorithm that directly optimizes various weighted graph clustering objectives, such as the popular ratio cut, normalized cut, and ratio association criteria. This eliminates the need for any eigenvector computation for graph clustering problems, which can be prohibitive for very large graphs. Previous multilevel graph partitioning methods, such as Metis, have suffered from the restriction of equal-sized clusters; our multilevel algorithm removes this restriction by using kernel k-means to optimize weighted graph cuts. Experimental results show that our multilevel algorithm outperforms a state-of-the-art spectral clustering algorithm in terms of speed, memory usage, and quality. We demonstrate that our algorithm is applicable to large-scale clustering tasks such as image segmentation, social network analysis and gene network analysis.

Detecting community structure via the maximal sub-graphs and belonging degrees in complex networks

NASA Astrophysics Data System (ADS)

Cui, Yaozu; Wang, Xingyuan; Eustace, Justine

2014-12-01

Community structure is a common phenomenon in complex networks, and it has been shown that some communities in complex networks often overlap each other. So in this paper we propose a new algorithm to detect overlapping community structure in complex networks. To identify the overlapping community structure, our algorithm firstly extracts fully connected sub-graphs which are maximal sub-graphs from original networks. Then two maximal sub-graphs having the key pair-vertices can be merged into a new larger sub-graph using some belonging degree functions. Furthermore we extend the modularity function to evaluate the proposed algorithm. In addition, overlapping nodes between communities are founded successfully. Finally we report the comparison between the modularity and the computational complexity of the proposed algorithm with some other existing algorithms. The experimental results show that the proposed algorithm gives satisfactory results.

BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

PubMed

Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of streamline tractography algorithms or the assumption of a noise distribution. Moreover, the BootGraph can be applied to common DTI data sets without further modifications and shows a high repeatability. Thus, it is very well suited for longitudinal studies and meta-studies based on DTI. Copyright © 2012 Elsevier Inc. All rights reserved.

Functional grouping of similar genes using eigenanalysis on minimum spanning tree based neighborhood graph.

PubMed

Jothi, R; Mohanty, Sraban Kumar; Ojha, Aparajita

2016-04-01

Gene expression data clustering is an important biological process in DNA microarray analysis. Although there have been many clustering algorithms for gene expression analysis, finding a suitable and effective clustering algorithm is always a challenging problem due to the heterogeneous nature of gene profiles. Minimum Spanning Tree (MST) based clustering algorithms have been successfully employed to detect clusters of varying shapes and sizes. This paper proposes a novel clustering algorithm using Eigenanalysis on Minimum Spanning Tree based neighborhood graph (E-MST). As MST of a set of points reflects the similarity of the points with their neighborhood, the proposed algorithm employs a similarity graph obtained from k(') rounds of MST (k(')-MST neighborhood graph). By studying the spectral properties of the similarity matrix obtained from k(')-MST graph, the proposed algorithm achieves improved clustering results. We demonstrate the efficacy of the proposed algorithm on 12 gene expression datasets. Experimental results show that the proposed algorithm performs better than the standard clustering algorithms. Copyright © 2016 Elsevier Ltd. All rights reserved.

Exact and approximate graph matching using random walks.

PubMed

Gori, Marco; Maggini, Marco; Sarti, Lorenzo

2005-07-01

In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

Stochastic generation of complex crystal structures combining group and graph theory with application to carbon

NASA Astrophysics Data System (ADS)

Shi, Xizhi; He, Chaoyu; Pickard, Chris J.; Tang, Chao; Zhong, Jianxin

2018-01-01

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold sp2 carbons, fourfold sp3 carbons, as well as mixed sp2-sp3 carbons. To demonstrate the method, we randomly construct initial structures adhering to space groups from 75 to 230 and a range of lattice constants, and we identify 281 new sp3 carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

Using ontology network structure in text mining.

PubMed

Berndt, Donald J; McCart, James A; Luther, Stephen L

2010-11-13

Statistical text mining treats documents as bags of words, with a focus on term frequencies within documents and across document collections. Unlike natural language processing (NLP) techniques that rely on an engineered vocabulary or a full-featured ontology, statistical approaches do not make use of domain-specific knowledge. The freedom from biases can be an advantage, but at the cost of ignoring potentially valuable knowledge. The approach proposed here investigates a hybrid strategy based on computing graph measures of term importance over an entire ontology and injecting the measures into the statistical text mining process. As a starting point, we adapt existing search engine algorithms such as PageRank and HITS to determine term importance within an ontology graph. The graph-theoretic approach is evaluated using a smoking data set from the i2b2 National Center for Biomedical Computing, cast as a simple binary classification task for categorizing smoking-related documents, demonstrating consistent improvements in accuracy.

An Energy-Efficient Target-Tracking Strategy for Mobile Sensor Networks.

PubMed

Mahboubi, Hamid; Masoudimansour, Walid; Aghdam, Amir G; Sayrafian-Pour, Kamran

2017-02-01

In this paper, an energy-efficient strategy is proposed for tracking a moving target in an environment with obstacles, using a network of mobile sensors. Typically, the most dominant sources of energy consumption in a mobile sensor network are sensing, communication, and movement. The proposed algorithm first divides the field into a grid of sufficiently small cells. The grid is then represented by a graph whose edges are properly weighted to reflect the energy consumption of sensors. The proposed technique searches for near-optimal locations for the sensors in different time instants to route information from the target to destination, using a shortest path algorithm. Simulations confirm the efficacy of the proposed algorithm.

Analyzing locomotion synthesis with feature-based motion graphs.

PubMed

Mahmudi, Mentar; Kallmann, Marcelo

2013-05-01

We propose feature-based motion graphs for realistic locomotion synthesis among obstacles. Among several advantages, feature-based motion graphs achieve improved results in search queries, eliminate the need of postprocessing for foot skating removal, and reduce the computational requirements in comparison to traditional motion graphs. Our contributions are threefold. First, we show that choosing transitions based on relevant features significantly reduces graph construction time and leads to improved search performances. Second, we employ a fast channel search method that confines the motion graph search to a free channel with guaranteed clearance among obstacles, achieving faster and improved results that avoid expensive collision checking. Lastly, we present a motion deformation model based on Inverse Kinematics applied over the transitions of a solution branch. Each transition is assigned a continuous deformation range that does not exceed the original transition cost threshold specified by the user for the graph construction. The obtained deformation improves the reachability of the feature-based motion graph and in turn also reduces the time spent during search. The results obtained by the proposed methods are evaluated and quantified, and they demonstrate significant improvements in comparison to traditional motion graph techniques.

Cooperative Search by UAV Teams: A Model Predictive Approach Using Dynamic Graphs

DTIC Science & Technology

2011-10-01

decentralized processing and control architecture. SLAMEM asset models accurately represent the Unicorn UAV platforms and other standard military platforms in...IMPLEMENTATION The CGBMPS algorithm has been successfully field-tested using both Unicorn [27] and Raven [20] UAV platforms. This section describes...the hardware-software system setup and implementation used for testing with Unicorns , Toyon’s UAV test platform. We also present some results from the

Multimodal Logistics Network Design over Planning Horizon through a Hybrid Meta-Heuristic Approach

NASA Astrophysics Data System (ADS)

Shimizu, Yoshiaki; Yamazaki, Yoshihiro; Wada, Takeshi

Logistics has been acknowledged increasingly as a key issue of supply chain management to improve business efficiency under global competition and diversified customer demands. This study aims at improving a quality of strategic decision making associated with dynamic natures in logistics network optimization. Especially, noticing an importance to concern with a multimodal logistics under multiterms, we have extended a previous approach termed hybrid tabu search (HybTS). The attempt intends to deploy a strategic planning more concretely so that the strategic plan can link to an operational decision making. The idea refers to a smart extension of the HybTS to solve a dynamic mixed integer programming problem. It is a two-level iterative method composed of a sophisticated tabu search for the location problem at the upper level and a graph algorithm for the route selection at the lower level. To keep efficiency while coping with the resulting extremely large-scale problem, we invented a systematic procedure to transform the original linear program at the lower-level into a minimum cost flow problem solvable by the graph algorithm. Through numerical experiments, we verified the proposed method outperformed the commercial software. The results indicate the proposed approach can make the conventional strategic decision much more practical and is promising for real world applications.

Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.

PubMed

Szalkai, Balázs; Varga, Bálint; Grolmusz, Vince

2015-01-01

Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges.

Graph Theoretical Analysis Reveals: Women’s Brains Are Better Connected than Men’s

PubMed Central

Szalkai, Balázs; Varga, Bálint; Grolmusz, Vince

2015-01-01

Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google’s PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges. PMID:26132764

Overlapping communities from dense disjoint and high total degree clusters

NASA Astrophysics Data System (ADS)

Zhang, Hongli; Gao, Yang; Zhang, Yue

2018-04-01

Community plays an important role in the field of sociology, biology and especially in domains of computer science, where systems are often represented as networks. And community detection is of great importance in the domains. A community is a dense subgraph of the whole graph with more links between its members than between its members to the outside nodes, and nodes in the same community probably share common properties or play similar roles in the graph. Communities overlap when nodes in a graph belong to multiple communities. A vast variety of overlapping community detection methods have been proposed in the literature, and the local expansion method is one of the most successful techniques dealing with large networks. The paper presents a density-based seeding method, in which dense disjoint local clusters are searched and selected as seeds. The proposed method selects a seed by the total degree and density of local clusters utilizing merely local structures of the network. Furthermore, this paper proposes a novel community refining phase via minimizing the conductance of each community, through which the quality of identified communities is largely improved in linear time. Experimental results in synthetic networks show that the proposed seeding method outperforms other seeding methods in the state of the art and the proposed refining method largely enhances the quality of the identified communities. Experimental results in real graphs with ground-truth communities show that the proposed approach outperforms other state of the art overlapping community detection algorithms, in particular, it is more than two orders of magnitude faster than the existing global algorithms with higher quality, and it obtains much more accurate community structure than the current local algorithms without any priori information.

Fast generation of sparse random kernel graphs

DOE PAGES

Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

2015-09-10

The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less

Discrete geometric analysis of message passing algorithm on graphs

NASA Astrophysics Data System (ADS)

Watanabe, Yusuke

2010-04-01

We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

MISAGA: An Algorithm for Mining Interesting Subgraphs in Attributed Graphs.

PubMed

He, Tiantian; Chan, Keith C C

2018-05-01

An attributed graph contains vertices that are associated with a set of attribute values. Mining clusters or communities, which are interesting subgraphs in the attributed graph is one of the most important tasks of graph analytics. Many problems can be defined as the mining of interesting subgraphs in attributed graphs. Algorithms that discover subgraphs based on predefined topologies cannot be used to tackle these problems. To discover interesting subgraphs in the attributed graph, we propose an algorithm called mining interesting subgraphs in attributed graph algorithm (MISAGA). MISAGA performs its tasks by first using a probabilistic measure to determine whether the strength of association between a pair of attribute values is strong enough to be interesting. Given the interesting pairs of attribute values, then the degree of association is computed for each pair of vertices using an information theoretic measure. Based on the edge structure and degree of association between each pair of vertices, MISAGA identifies interesting subgraphs by formulating it as a constrained optimization problem and solves it by identifying the optimal affiliation of subgraphs for the vertices in the attributed graph. MISAGA has been tested with several large-sized real graphs and is found to be potentially very useful for various applications.

EAGLE: 'EAGLE'Is an' Algorithmic Graph Library for Exploration

DOE Office of Scientific and Technical Information (OSTI.GOV)

2015-01-16

The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. Today there is no tools to conduct "graph mining" on RDF standard data sets. We address that need through implementation of popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, degree distribution,more » diversity degree, PageRank, etc.). We implement these algorithms as SPARQL queries, wrapped within Python scripts and call our software tool as EAGLE. In RDF style, EAGLE stands for "EAGLE 'Is an' algorithmic graph library for exploration. EAGLE is like 'MATLAB' for 'Linked Data.'« less

Approximate Computing Techniques for Iterative Graph Algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

Label-based routing for a family of small-world Farey graphs.

PubMed

Zhai, Yinhu; Wang, Yinhe

2016-05-11

We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.

Label-based routing for a family of small-world Farey graphs

NASA Astrophysics Data System (ADS)

Zhai, Yinhu; Wang, Yinhe

2016-05-01

We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.

Efficient enumeration of monocyclic chemical graphs with given path frequencies

PubMed Central

2014-01-01

Background The enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics because it leads to a variety of useful applications including structure determination and development of novel chemical compounds. Results We consider the problem of enumerating chemical graphs with monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors, where a feature vector represents the frequency of the prescribed paths in a chemical compound to be constructed and the set is specified by a pair of upper and lower feature vectors. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending these algorithms to enumeration of chemical graphs with monocyclic structure by designing a fast algorithm for testing uniqueness. The results of computational experiments reveal that the computational efficiency of the new algorithm is as good as those for enumeration of tree-like chemical compounds. Conclusions We succeed in expanding the class of chemical graphs that are able to be enumerated efficiently. PMID:24955135

BFL: a node and edge betweenness based fast layout algorithm for large scale networks

PubMed Central

Hashimoto, Tatsunori B; Nagasaki, Masao; Kojima, Kaname; Miyano, Satoru

2009-01-01

Background Network visualization would serve as a useful first step for analysis. However, current graph layout algorithms for biological pathways are insensitive to biologically important information, e.g. subcellular localization, biological node and graph attributes, or/and not available for large scale networks, e.g. more than 10000 elements. Results To overcome these problems, we propose the use of a biologically important graph metric, betweenness, a measure of network flow. This metric is highly correlated with many biological phenomena such as lethality and clusters. We devise a new fast parallel algorithm calculating betweenness to minimize the preprocessing cost. Using this metric, we also invent a node and edge betweenness based fast layout algorithm (BFL). BFL places the high-betweenness nodes to optimal positions and allows the low-betweenness nodes to reach suboptimal positions. Furthermore, BFL reduces the runtime by combining a sequential insertion algorim with betweenness. For a graph with n nodes, this approach reduces the expected runtime of the algorithm to O(n2) when considering edge crossings, and to O(n log n) when considering only density and edge lengths. Conclusion Our BFL algorithm is compared against fast graph layout algorithms and approaches requiring intensive optimizations. For gene networks, we show that our algorithm is faster than all layout algorithms tested while providing readability on par with intensive optimization algorithms. We achieve a 1.4 second runtime for a graph with 4000 nodes and 12000 edges on a standard desktop computer. PMID:19146673

Automated boundary detection of the optic disc and layer segmentation of the peripapillary retina in volumetric structural and angiographic optical coherence tomography.

PubMed

Zang, Pengxiao; Gao, Simon S; Hwang, Thomas S; Flaxel, Christina J; Wilson, David J; Morrison, John C; Huang, David; Li, Dengwang; Jia, Yali

2017-03-01

To improve optic disc boundary detection and peripapillary retinal layer segmentation, we propose an automated approach for structural and angiographic optical coherence tomography. The algorithm was performed on radial cross-sectional B-scans. The disc boundary was detected by searching for the position of Bruch's membrane opening, and retinal layer boundaries were detected using a dynamic programming-based graph search algorithm on each B-scan without the disc region. A comparison of the disc boundary using our method with that determined by manual delineation showed good accuracy, with an average Dice similarity coefficient ≥0.90 in healthy eyes and eyes with diabetic retinopathy and glaucoma. The layer segmentation accuracy in the same cases was on average less than one pixel (3.13 μm).

Automated boundary detection of the optic disc and layer segmentation of the peripapillary retina in volumetric structural and angiographic optical coherence tomography

PubMed Central

Zang, Pengxiao; Gao, Simon S.; Hwang, Thomas S.; Flaxel, Christina J.; Wilson, David J.; Morrison, John C.; Huang, David; Li, Dengwang; Jia, Yali

2017-01-01

To improve optic disc boundary detection and peripapillary retinal layer segmentation, we propose an automated approach for structural and angiographic optical coherence tomography. The algorithm was performed on radial cross-sectional B-scans. The disc boundary was detected by searching for the position of Bruch’s membrane opening, and retinal layer boundaries were detected using a dynamic programming-based graph search algorithm on each B-scan without the disc region. A comparison of the disc boundary using our method with that determined by manual delineation showed good accuracy, with an average Dice similarity coefficient ≥0.90 in healthy eyes and eyes with diabetic retinopathy and glaucoma. The layer segmentation accuracy in the same cases was on average less than one pixel (3.13 μm). PMID:28663830

Information spread of emergency events: path searching on social networks.

PubMed

Dai, Weihui; Hu, Hongzhi; Wu, Tunan; Dai, Yonghui

2014-01-01

Emergency has attracted global attentions of government and the public, and it will easily trigger a series of serious social problems if it is not supervised effectively in the dissemination process. In the Internet world, people communicate with each other and form various virtual communities based on social networks, which lead to a complex and fast information spread pattern of emergency events. This paper collects Internet data based on data acquisition and topic detection technology, analyzes the process of information spread on social networks, describes the diffusions and impacts of that information from the perspective of random graph, and finally seeks the key paths through an improved IBF algorithm. Application cases have shown that this algorithm can search the shortest spread paths efficiently, which may help us to guide and control the information dissemination of emergency events on early warning.

Visual Exploratory Search of Relationship Graphs on Smartphones

PubMed Central

Ouyang, Jianquan; Zheng, Hao; Kong, Fanbin; Liu, Tianming

2013-01-01

This paper presents a novel framework for Visual Exploratory Search of Relationship Graphs on Smartphones (VESRGS) that is composed of three major components: inference and representation of semantic relationship graphs on the Web via meta-search, visual exploratory search of relationship graphs through both querying and browsing strategies, and human-computer interactions via the multi-touch interface and mobile Internet on smartphones. In comparison with traditional lookup search methodologies, the proposed VESRGS system is characterized with the following perceived advantages. 1) It infers rich semantic relationships between the querying keywords and other related concepts from large-scale meta-search results from Google, Yahoo! and Bing search engines, and represents semantic relationships via graphs; 2) the exploratory search approach empowers users to naturally and effectively explore, adventure and discover knowledge in a rich information world of interlinked relationship graphs in a personalized fashion; 3) it effectively takes the advantages of smartphones’ user-friendly interfaces and ubiquitous Internet connection and portability. Our extensive experimental results have demonstrated that the VESRGS framework can significantly improve the users’ capability of seeking the most relevant relationship information to their own specific needs. We envision that the VESRGS framework can be a starting point for future exploration of novel, effective search strategies in the mobile Internet era. PMID:24223936

LDRD final report :

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brost, Randolph C.; McLendon, William Clarence,

2013-01-01

Modeling geospatial information with semantic graphs enables search for sites of interest based on relationships between features, without requiring strong a priori models of feature shape or other intrinsic properties. Geospatial semantic graphs can be constructed from raw sensor data with suitable preprocessing to obtain a discretized representation. This report describes initial work toward extending geospatial semantic graphs to include temporal information, and initial results applying semantic graph techniques to SAR image data. We describe an efficient graph structure that includes geospatial and temporal information, which is designed to support simultaneous spatial and temporal search queries. We also report amore » preliminary implementation of feature recognition, semantic graph modeling, and graph search based on input SAR data. The report concludes with lessons learned and suggestions for future improvements.« less

A DAG Scheduling Scheme on Heterogeneous Computing Systems Using Tuple-Based Chemical Reaction Optimization

PubMed Central

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

A complex computing problem can be solved efficiently on a system with multiple computing nodes by dividing its implementation code into several parallel processing modules or tasks that can be formulated as directed acyclic graph (DAG) problems. The DAG jobs may be mapped to and scheduled on the computing nodes to minimize the total execution time. Searching an optimal DAG scheduling solution is considered to be NP-complete. This paper proposed a tuple molecular structure-based chemical reaction optimization (TMSCRO) method for DAG scheduling on heterogeneous computing systems, based on a very recently proposed metaheuristic method, chemical reaction optimization (CRO). Comparing with other CRO-based algorithms for DAG scheduling, the design of tuple reaction molecular structure and four elementary reaction operators of TMSCRO is more reasonable. TMSCRO also applies the concept of constrained critical paths (CCPs), constrained-critical-path directed acyclic graph (CCPDAG) and super molecule for accelerating convergence. In this paper, we have also conducted simulation experiments to verify the effectiveness and efficiency of TMSCRO upon a large set of randomly generated graphs and the graphs for real world problems. PMID:25143977

A DAG scheduling scheme on heterogeneous computing systems using tuple-based chemical reaction optimization.

PubMed

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

A complex computing problem can be solved efficiently on a system with multiple computing nodes by dividing its implementation code into several parallel processing modules or tasks that can be formulated as directed acyclic graph (DAG) problems. The DAG jobs may be mapped to and scheduled on the computing nodes to minimize the total execution time. Searching an optimal DAG scheduling solution is considered to be NP-complete. This paper proposed a tuple molecular structure-based chemical reaction optimization (TMSCRO) method for DAG scheduling on heterogeneous computing systems, based on a very recently proposed metaheuristic method, chemical reaction optimization (CRO). Comparing with other CRO-based algorithms for DAG scheduling, the design of tuple reaction molecular structure and four elementary reaction operators of TMSCRO is more reasonable. TMSCRO also applies the concept of constrained critical paths (CCPs), constrained-critical-path directed acyclic graph (CCPDAG) and super molecule for accelerating convergence. In this paper, we have also conducted simulation experiments to verify the effectiveness and efficiency of TMSCRO upon a large set of randomly generated graphs and the graphs for real world problems.

Decomposition Algorithm for Global Reachability Analysis on a Time-Varying Graph with an Application to Planetary Exploration

NASA Technical Reports Server (NTRS)

Kuwata, Yoshiaki; Blackmore, Lars; Wolf, Michael; Fathpour, Nanaz; Newman, Claire; Elfes, Alberto

2009-01-01

Hot air (Montgolfiere) balloons represent a promising vehicle system for possible future exploration of planets and moons with thick atmospheres such as Venus and Titan. To go to a desired location, this vehicle can primarily use the horizontal wind that varies with altitude, with a small help of its own actuation. A main challenge is how to plan such trajectory in a highly nonlinear and time-varying wind field. This paper poses this trajectory planning as a graph search on the space-time grid and addresses its computational aspects. When capturing various time scales involved in the wind field over the duration of long exploration mission, the size of the graph becomes excessively large. We show that the adjacency matrix of the graph is block-triangular, and by exploiting this structure, we decompose the large planning problem into several smaller subproblems, whose memory requirement stays almost constant as the problem size grows. The approach is demonstrated on a global reachability analysis of a possible Titan mission scenario.

Human-Robot Teams Informed by Human Performance Moderator Functions

DTIC Science & Technology

2012-08-29

seem to converge probably because situation is bad enough that any algorithm would perform just as well. Figure 29 shows the set commonality graph...burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing...for writing the report, performing the research, or credited with the content of the report. The form of entry is the last name, first name, middle

A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph

PubMed Central

Pan, Yongke; Niu, Wenjia

2017-01-01

Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines. PMID:28316616

Collaborative mining and transfer learning for relational data

NASA Astrophysics Data System (ADS)

Levchuk, Georgiy; Eslami, Mohammed

2015-06-01

Many of the real-world problems, - including human knowledge, communication, biological, and cyber network analysis, - deal with data entities for which the essential information is contained in the relations among those entities. Such data must be modeled and analyzed as graphs, with attributes on both objects and relations encode and differentiate their semantics. Traditional data mining algorithms were originally designed for analyzing discrete objects for which a set of features can be defined, and thus cannot be easily adapted to deal with graph data. This gave rise to the relational data mining field of research, of which graph pattern learning is a key sub-domain [11]. In this paper, we describe a model for learning graph patterns in collaborative distributed manner. Distributed pattern learning is challenging due to dependencies between the nodes and relations in the graph, and variability across graph instances. We present three algorithms that trade-off benefits of parallelization and data aggregation, compare their performance to centralized graph learning, and discuss individual benefits and weaknesses of each model. Presented algorithms are designed for linear speedup in distributed computing environments, and learn graph patterns that are both closer to ground truth and provide higher detection rates than centralized mining algorithm.

Assessing the impact of background spectral graph construction techniques on the topological anomaly detection algorithm

NASA Astrophysics Data System (ADS)

Ziemann, Amanda K.; Messinger, David W.; Albano, James A.; Basener, William F.

2012-06-01

Anomaly detection algorithms have historically been applied to hyperspectral imagery in order to identify pixels whose material content is incongruous with the background material in the scene. Typically, the application involves extracting man-made objects from natural and agricultural surroundings. A large challenge in designing these algorithms is determining which pixels initially constitute the background material within an image. The topological anomaly detection (TAD) algorithm constructs a graph theory-based, fully non-parametric topological model of the background in the image scene, and uses codensity to measure deviation from this background. In TAD, the initial graph theory structure of the image data is created by connecting an edge between any two pixel vertices x and y if the Euclidean distance between them is less than some resolution r. While this type of proximity graph is among the most well-known approaches to building a geometric graph based on a given set of data, there is a wide variety of dierent geometrically-based techniques. In this paper, we present a comparative test of the performance of TAD across four dierent constructs of the initial graph: mutual k-nearest neighbor graph, sigma-local graph for two different values of σ > 1, and the proximity graph originally implemented in TAD.

Faster Parameterized Algorithms for Minor Containment

NASA Astrophysics Data System (ADS)

Adler, Isolde; Dorn, Frederic; Fomin, Fedor V.; Sau, Ignasi; Thilikos, Dimitrios M.

The theory of Graph Minors by Robertson and Seymour is one of the deepest and significant theories in modern Combinatorics. This theory has also a strong impact on the recent development of Algorithms, and several areas, like Parameterized Complexity, have roots in Graph Minors. Until very recently it was a common belief that Graph Minors Theory is mainly of theoretical importance. However, it appears that many deep results from Robertson and Seymour's theory can be also used in the design of practical algorithms. Minor containment testing is one of algorithmically most important and technical parts of the theory, and minor containment in graphs of bounded branchwidth is a basic ingredient of this algorithm. In order to implement minor containment testing on graphs of bounded branchwidth, Hicks [NETWORKS 04] described an algorithm, that in time O(3^{k^2}\\cdot (h+k-1)!\\cdot m) decides if a graph G with m edges and branchwidth k, contains a fixed graph H on h vertices as a minor. That algorithm follows the ideas introduced by Robertson and Seymour in [J'CTSB 95]. In this work we improve the dependence on k of Hicks' result by showing that checking if H is a minor of G can be done in time O(2^{(2k +1 )\\cdot log k} \\cdot h^{2k} \\cdot 2^{2h^2} \\cdot m). Our approach is based on a combinatorial object called rooted packing, which captures the properties of the potential models of subgraphs of H that we seek in our dynamic programming algorithm. This formulation with rooted packings allows us to speed up the algorithm when G is embedded in a fixed surface, obtaining the first single-exponential algorithm for minor containment testing. Namely, it runs in time 2^{O(k)} \\cdot h^{2k} \\cdot 2^{O(h)} \\cdot n, with n = |V(G)|. Finally, we show that slight modifications of our algorithm permit to solve some related problems within the same time bounds, like induced minor or contraction minor containment.

Thread Graphs, Linear Rank-Width and Their Algorithmic Applications

NASA Astrophysics Data System (ADS)

Ganian, Robert

The introduction of tree-width by Robertson and Seymour [7] was a breakthrough in the design of graph algorithms. A lot of research since then has focused on obtaining a width measure which would be more general and still allowed efficient algorithms for a wide range of NP-hard problems on graphs of bounded width. To this end, Oum and Seymour have proposed rank-width, which allows the solution of many such hard problems on a less restricted graph classes (see e.g. [3,4]). But what about problems which are NP-hard even on graphs of bounded tree-width or even on trees? The parameter used most often for these exceptionally hard problems is path-width, however it is extremely restrictive - for example the graphs of path-width 1 are exactly paths.

Graphing Online Searches with Lotus 1-2-3.

ERIC Educational Resources Information Center

Persson, Olle

1986-01-01

This article illustrates how Lotus 1-2-3 software can be used to create graphs using downloaded online searches as raw material, notes most commands applied, and outlines three required steps: downloading, importing the downloading file into the worksheet, and making graphs. An example in bibliometrics and sample graphs are included. (EJS)

A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choudhury, Sutanay; Holder, Larry; Chin, George

2015-05-27

Cyber security is one of the most significant technical challenges in current times. Detecting adversarial activities, prevention of theft of intellectual properties and customer data is a high priority for corporations and government agencies around the world. Cyber defenders need to analyze massive-scale, high-resolution network flows to identify, categorize, and mitigate attacks involving networks spanning institutional and national boundaries. Many of the cyber attacks can be described as subgraph patterns, with prominent examples being insider infiltrations (path queries), denial of service (parallel paths) and malicious spreads (tree queries). This motivates us to explore subgraph matching on streaming graphs in amore » continuous setting. The novelty of our work lies in using the subgraph distributional statistics collected from the streaming graph to determine the query processing strategy. We introduce a ``Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named ``Relative Selectivity" that is used to select between different query processing strategies. Our experiments performed on real online news, network traffic stream and a synthetic social network benchmark demonstrate 10-100x speedups over non-incremental, selectivity agnostic approaches.« less

Bounded-Degree Approximations of Stochastic Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less

A Coherent VLSI Environment

DTIC Science & Technology

1987-03-31

processors . The symmetry-breaking algorithms give efficient ways to convert probabilistic algorithms to deterministic algorithms. Some of the...techniques have been applied to construct several efficient linear- processor algorithms for graph problems, including an O(lg* n)-time algorithm for (A + 1...On n-node graphs, the algorithm works in O(log 2 n) time using only n processors , in contrast to the previous best algorithm which used about n3

A Novel Discrete Differential Evolution Algorithm for the Vehicle Routing Problem in B2C E-Commerce

NASA Astrophysics Data System (ADS)

Xia, Chao; Sheng, Ying; Jiang, Zhong-Zhong; Tan, Chunqiao; Huang, Min; He, Yuanjian

2015-12-01

In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the vehicle routing problems (VRP) in B2C e-commerce, in which VRP is modeled by the incomplete graph based on the actual urban road system. First, a variant of classical VRP is described and a mathematical programming model for the variant is given. Second, the DDE is presented, where individuals are represented as the sequential encoding scheme, and a novel reparation operator is employed to repair the infeasible solutions. Furthermore, a FLOYD operator for dealing with the shortest route is embedded in the proposed DDE. Finally, an extensive computational study is carried out in comparison with the predatory search algorithm and genetic algorithm, and the results show that the proposed DDE is an effective algorithm for VRP in B2C e-commerce.

Automatic classification of protein structures relying on similarities between alignments

PubMed Central

2012-01-01

Background Identification of protein structural cores requires isolation of sets of proteins all sharing a same subset of structural motifs. In the context of an ever growing number of available 3D protein structures, standard and automatic clustering algorithms require adaptations so as to allow for efficient identification of such sets of proteins. Results When considering a pair of 3D structures, they are stated as similar or not according to the local similarities of their matching substructures in a structural alignment. This binary relation can be represented in a graph of similarities where a node represents a 3D protein structure and an edge states that two 3D protein structures are similar. Therefore, classifying proteins into structural families can be viewed as a graph clustering task. Unfortunately, because such a graph encodes only pairwise similarity information, clustering algorithms may include in the same cluster a subset of 3D structures that do not share a common substructure. In order to overcome this drawback we first define a ternary similarity on a triple of 3D structures as a constraint to be satisfied by the graph of similarities. Such a ternary constraint takes into account similarities between pairwise alignments, so as to ensure that the three involved protein structures do have some common substructure. We propose hereunder a modification algorithm that eliminates edges from the original graph of similarities and gives a reduced graph in which no ternary constraints are violated. Our approach is then first to build a graph of similarities, then to reduce the graph according to the modification algorithm, and finally to apply to the reduced graph a standard graph clustering algorithm. Such method was used for classifying ASTRAL-40 non-redundant protein domains, identifying significant pairwise similarities with Yakusa, a program devised for rapid 3D structure alignments. Conclusions We show that filtering similarities prior to standard graph based clustering process by applying ternary similarity constraints i) improves the separation of proteins of different classes and consequently ii) improves the classification quality of standard graph based clustering algorithms according to the reference classification SCOP. PMID:22974051

A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains

NASA Astrophysics Data System (ADS)

Gan, Tingyue; Cameron, Maria

2017-06-01

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical timescales at which the qualitative behavior of a given Markov chain changes, and give an effective description of the dynamics on each of them. This approach is valid for both time-reversible and time-irreversible Markov processes, with or without symmetry. Central to this approach are two graph algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the critical timescales and the hierarchies of Typical Transition Graphs or T-graphs indicating the most likely transitions in the system without and with symmetry, respectively. The sequence of critical timescales includes the subsequence of the reciprocals of the real parts of eigenvalues. Under a certain assumption, we prove sharp asymptotic estimates for eigenvalues (including pre-factors) and show how one can extract them from the output of Algorithm 1. We discuss the relationship between Algorithms 1 and 2 and explain how one needs to interpret the output of Algorithm 1 if it is applied in the case with symmetry instead of Algorithm 2. Finally, we analyze an example motivated by R. D. Astumian's model of the dynamics of kinesin, a molecular motor, by means of Algorithm 2.

Application-Specific Graph Sampling for Frequent Subgraph Mining and Community Detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purohit, Sumit; Choudhury, Sutanay; Holder, Lawrence B.

Graph mining is an important data analysis methodology, but struggles as the input graph size increases. The scalability and usability challenges posed by such large graphs make it imperative to sample the input graph and reduce its size. The critical challenge in sampling is to identify the appropriate algorithm to insure the resulting analysis does not suffer heavily from the data reduction. Predicting the expected performance degradation for a given graph and sampling algorithm is also useful. In this paper, we present different sampling approaches for graph mining applications such as Frequent Subgrpah Mining (FSM), and Community Detection (CD). Wemore » explore graph metrics such as PageRank, Triangles, and Diversity to sample a graph and conclude that for heterogeneous graphs Triangles and Diversity perform better than degree based metrics. We also present two new sampling variations for targeted graph mining applications. We present empirical results to show that knowledge of the target application, along with input graph properties can be used to select the best sampling algorithm. We also conclude that performance degradation is an abrupt, rather than gradual phenomena, as the sample size decreases. We present the empirical results to show that the performance degradation follows a logistic function.« less

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

PubMed

He, Chenlong; Feng, Zuren; Ren, Zhigang

2018-01-01

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions

PubMed Central

Feng, Zuren; Ren, Zhigang

2018-01-01

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared. PMID:29462217

Enhancing SAMOS Data Access in DOMS via a Neo4j Property Graph Database.

NASA Astrophysics Data System (ADS)

Stallard, A. P.; Smith, S. R.; Elya, J. L.

2016-12-01

The Shipboard Automated Meteorological and Oceanographic System (SAMOS) initiative provides routine access to high-quality marine meteorological and near-surface oceanographic observations from research vessels. The Distributed Oceanographic Match-Up Service (DOMS) under development is a centralized service that allows researchers to easily match in situ and satellite oceanographic data from distributed sources to facilitate satellite calibration, validation, and retrieval algorithm development. The service currently uses Apache Solr as a backend search engine on each node in the distributed network. While Solr is a high-performance solution that facilitates creation and maintenance of indexed data, it is limited in the sense that its schema is fixed. The property graph model escapes this limitation by creating relationships between data objects. The authors will present the development of the SAMOS Neo4j property graph database including new search possibilities that take advantage of the property graph model, performance comparisons with Apache Solr, and a vision for graph databases as a storage tool for oceanographic data. The integration of the SAMOS Neo4j graph into DOMS will also be described. Currently, Neo4j contains spatial and temporal records from SAMOS which are modeled into a time tree and r-tree using Graph Aware and Spatial plugin tools for Neo4j. These extensions provide callable Java procedures within CYPHER (Neo4j's query language) that generate in-graph structures. Once generated, these structures can be queried using procedures from these libraries, or directly via CYPHER statements. Neo4j excels at performing relationship and path-based queries, which challenge relational-SQL databases because they require memory intensive joins due to the limitation of their design. Consider a user who wants to find records over several years, but only for specific months. If a traditional database only stores timestamps, this type of query would be complex and likely prohibitively slow. Using the time tree model, one can specify a path from the root to the data which restricts resolutions to certain timeframes (e.g., months). This query can be executed without joins, unions, or other compute-intensive operations, putting Neo4j at a computational advantage to the SQL database alternative.

Information Spread of Emergency Events: Path Searching on Social Networks

PubMed Central

Hu, Hongzhi; Wu, Tunan

2014-01-01

Emergency has attracted global attentions of government and the public, and it will easily trigger a series of serious social problems if it is not supervised effectively in the dissemination process. In the Internet world, people communicate with each other and form various virtual communities based on social networks, which lead to a complex and fast information spread pattern of emergency events. This paper collects Internet data based on data acquisition and topic detection technology, analyzes the process of information spread on social networks, describes the diffusions and impacts of that information from the perspective of random graph, and finally seeks the key paths through an improved IBF algorithm. Application cases have shown that this algorithm can search the shortest spread paths efficiently, which may help us to guide and control the information dissemination of emergency events on early warning. PMID:24600323

Optimizing Search and Ranking in Folksonomy Systems by Exploiting Context Information

NASA Astrophysics Data System (ADS)

Abel, Fabian; Henze, Nicola; Krause, Daniel

Tagging systems enable users to annotate resources with freely chosen keywords. The evolving bunch of tag assignments is called folksonomy and there exist already some approaches that exploit folksonomies to improve resource retrieval. In this paper, we analyze and compare graph-based ranking algorithms: FolkRank and SocialPageRank. We enhance these algorithms by exploiting the context of tags, and evaluate the results on the GroupMe! dataset. In GroupMe!, users can organize and maintain arbitrary Web resources in self-defined groups. When users annotate resources in GroupMe!, this can be interpreted in context of a certain group. The grouping activity itself is easy for users to perform. However, it delivers valuable semantic information about resources and their context. We present GRank that uses the context information to improve and optimize the detection of relevant search results, and compare different strategies for ranking result lists in folksonomy systems.

RNA Graph Partitioning for the Discovery of RNA Modularity: A Novel Application of Graph Partition Algorithm to Biology

PubMed Central

Elmetwaly, Shereef; Schlick, Tamar

2014-01-01

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2′s components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2′s components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs. PMID:25188578

Graph Mining Meets the Semantic Web

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Sangkeun; Sukumar, Sreenivas R; Lim, Seung-Hwan

The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluatemore » the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.« less

A comparison of graph- and kernel-based -omics data integration algorithms for classifying complex traits.

PubMed

Yan, Kang K; Zhao, Hongyu; Pang, Herbert

2017-12-06

High-throughput sequencing data are widely collected and analyzed in the study of complex diseases in quest of improving human health. Well-studied algorithms mostly deal with single data source, and cannot fully utilize the potential of these multi-omics data sources. In order to provide a holistic understanding of human health and diseases, it is necessary to integrate multiple data sources. Several algorithms have been proposed so far, however, a comprehensive comparison of data integration algorithms for classification of binary traits is currently lacking. In this paper, we focus on two common classes of integration algorithms, graph-based that depict relationships with subjects denoted by nodes and relationships denoted by edges, and kernel-based that can generate a classifier in feature space. Our paper provides a comprehensive comparison of their performance in terms of various measurements of classification accuracy and computation time. Seven different integration algorithms, including graph-based semi-supervised learning, graph sharpening integration, composite association network, Bayesian network, semi-definite programming-support vector machine (SDP-SVM), relevance vector machine (RVM) and Ada-boost relevance vector machine are compared and evaluated with hypertension and two cancer data sets in our study. In general, kernel-based algorithms create more complex models and require longer computation time, but they tend to perform better than graph-based algorithms. The performance of graph-based algorithms has the advantage of being faster computationally. The empirical results demonstrate that composite association network, relevance vector machine, and Ada-boost RVM are the better performers. We provide recommendations on how to choose an appropriate algorithm for integrating data from multiple sources.

Families of Graph Algorithms: SSSP Case Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanewala Appuhamilage, Thejaka Amila Jay; Zalewski, Marcin J.; Lumsdaine, Andrew

2017-08-28

Single-Source Shortest Paths (SSSP) is a well-studied graph problem. Examples of SSSP algorithms include the original Dijkstra’s algorithm and the parallel Δ-stepping and KLA-SSSP algorithms. In this paper, we use a novel Abstract Graph Machine (AGM) model to show that all these algorithms share a common logic and differ from one another by the order in which they perform work. We use the AGM model to thoroughly analyze the family of algorithms that arises from the common logic. We start with the basic algorithm without any ordering (Chaotic), and then we derive the existing and new algorithms by methodically exploringmore » semantic and spatial ordering of work. Our experimental results show that new derived algorithms show better performance than the existing distributed memory parallel algorithms, especially at higher scales.« less

Partitioning sparse matrices with eigenvectors of graphs

NASA Technical Reports Server (NTRS)

Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu

1990-01-01

The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.

Reproducibility of graph metrics of human brain structural networks.

PubMed

Duda, Jeffrey T; Cook, Philip A; Gee, James C

2014-01-01

Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.

Querying graphs in protein-protein interactions networks using feedback vertex set.

PubMed

Blin, Guillaume; Sikora, Florian; Vialette, Stéphane

2010-01-01

Recent techniques increase rapidly the amount of our knowledge on interactions between proteins. The interpretation of these new information depends on our ability to retrieve known substructures in the data, the Protein-Protein Interactions (PPIs) networks. In an algorithmic point of view, it is an hard task since it often leads to NP-hard problems. To overcome this difficulty, many authors have provided tools for querying patterns with a restricted topology, i.e., paths or trees in PPI networks. Such restriction leads to the development of fixed parameter tractable (FPT) algorithms, which can be practicable for restricted sizes of queries. Unfortunately, Graph Homomorphism is a W[1]-hard problem, and hence, no FPT algorithm can be found when patterns are in the shape of general graphs. However, Dost et al. gave an algorithm (which is not implemented) to query graphs with a bounded treewidth in PPI networks (the treewidth of the query being involved in the time complexity). In this paper, we propose another algorithm for querying pattern in the shape of graphs, also based on dynamic programming and the color-coding technique. To transform graphs queries into trees without loss of informations, we use feedback vertex set coupled to a node duplication mechanism. Hence, our algorithm is FPT for querying graphs with a bounded size of their feedback vertex set. It gives an alternative to the treewidth parameter, which can be better or worst for a given query. We provide a python implementation which allows us to validate our implementation on real data. Especially, we retrieve some human queries in the shape of graphs into the fly PPI network.

Regularized Embedded Multiple Kernel Dimensionality Reduction for Mine Signal Processing.

PubMed

Li, Shuang; Liu, Bing; Zhang, Chen

2016-01-01

Traditional multiple kernel dimensionality reduction models are generally based on graph embedding and manifold assumption. But such assumption might be invalid for some high-dimensional or sparse data due to the curse of dimensionality, which has a negative influence on the performance of multiple kernel learning. In addition, some models might be ill-posed if the rank of matrices in their objective functions was not high enough. To address these issues, we extend the traditional graph embedding framework and propose a novel regularized embedded multiple kernel dimensionality reduction method. Different from the conventional convex relaxation technique, the proposed algorithm directly takes advantage of a binary search and an alternative optimization scheme to obtain optimal solutions efficiently. The experimental results demonstrate the effectiveness of the proposed method for supervised, unsupervised, and semisupervised scenarios.

Dataflow Design Tool: User's Manual

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1996-01-01

The Dataflow Design Tool is a software tool for selecting a multiprocessor scheduling solution for a class of computational problems. The problems of interest are those that can be described with a dataflow graph and are intended to be executed repetitively on a set of identical processors. Typical applications include signal processing and control law problems. The software tool implements graph-search algorithms and analysis techniques based on the dataflow paradigm. Dataflow analyses provided by the software are introduced and shown to effectively determine performance bounds, scheduling constraints, and resource requirements. The software tool provides performance optimization through the inclusion of artificial precedence constraints among the schedulable tasks. The user interface and tool capabilities are described. Examples are provided to demonstrate the analysis, scheduling, and optimization functions facilitated by the tool.

A genetic graph-based approach for partitional clustering.

PubMed

Menéndez, Héctor D; Barrero, David F; Camacho, David

2014-05-01

Clustering is one of the most versatile tools for data analysis. In the recent years, clustering that seeks the continuity of data (in opposition to classical centroid-based approaches) has attracted an increasing research interest. It is a challenging problem with a remarkable practical interest. The most popular continuity clustering method is the spectral clustering (SC) algorithm, which is based on graph cut: It initially generates a similarity graph using a distance measure and then studies its graph spectrum to find the best cut. This approach is sensitive to the parameters of the metric, and a correct parameter choice is critical to the quality of the cluster. This work proposes a new algorithm, inspired by SC, that reduces the parameter dependency while maintaining the quality of the solution. The new algorithm, named genetic graph-based clustering (GGC), takes an evolutionary approach introducing a genetic algorithm (GA) to cluster the similarity graph. The experimental validation shows that GGC increases robustness of SC and has competitive performance in comparison with classical clustering methods, at least, in the synthetic and real dataset used in the experiments.

An experimental study of graph connectivity for unsupervised word sense disambiguation.

PubMed

Navigli, Roberto; Lapata, Mirella

2010-04-01

Word sense disambiguation (WSD), the task of identifying the intended meanings (senses) of words in context, has been a long-standing research objective for natural language processing. In this paper, we are concerned with graph-based algorithms for large-scale WSD. Under this framework, finding the right sense for a given word amounts to identifying the most "important" node among the set of graph nodes representing its senses. We introduce a graph-based WSD algorithm which has few parameters and does not require sense-annotated data for training. Using this algorithm, we investigate several measures of graph connectivity with the aim of identifying those best suited for WSD. We also examine how the chosen lexicon and its connectivity influences WSD performance. We report results on standard data sets and show that our graph-based approach performs comparably to the state of the art.

The graph neural network model.

PubMed

Scarselli, Franco; Gori, Marco; Tsoi, Ah Chung; Hagenbuchner, Markus; Monfardini, Gabriele

2009-01-01

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation

PubMed Central

Lee, Jae H.; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T.; Seo, Youngho

2014-01-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting. PMID:27081299

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation.

PubMed

Lee, Jae H; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T; Seo, Youngho

2014-11-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting.

Incremental k-core decomposition: Algorithms and evaluation

DOE PAGES

Sariyuce, Ahmet Erdem; Gedik, Bugra; Jacques-SIlva, Gabriela; ...

2016-02-01

A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for dynamic graph data. In this paper, we propose a suite of incremental k-core decomposition algorithms for dynamic graph data. These algorithms locate a small subgraph that ismore » guaranteed to contain the list of vertices whose maximum k-core values have changed and efficiently process this subgraph to update the k-core decomposition. We present incremental algorithms for both insertion and deletion operations, and propose auxiliary vertex state maintenance techniques that can further accelerate these operations. Our results show a significant reduction in runtime compared to non-incremental alternatives. We illustrate the efficiency of our algorithms on different types of real and synthetic graphs, at varying scales. Furthermore, for a graph of 16 million vertices, we observe relative throughputs reaching a million times, relative to the non-incremental algorithms.« less

Multi-label literature classification based on the Gene Ontology graph.

PubMed

Jin, Bo; Muller, Brian; Zhai, Chengxiang; Lu, Xinghua

2008-12-08

The Gene Ontology is a controlled vocabulary for representing knowledge related to genes and proteins in a computable form. The current effort of manually annotating proteins with the Gene Ontology is outpaced by the rate of accumulation of biomedical knowledge in literature, which urges the development of text mining approaches to facilitate the process by automatically extracting the Gene Ontology annotation from literature. The task is usually cast as a text classification problem, and contemporary methods are confronted with unbalanced training data and the difficulties associated with multi-label classification. In this research, we investigated the methods of enhancing automatic multi-label classification of biomedical literature by utilizing the structure of the Gene Ontology graph. We have studied three graph-based multi-label classification algorithms, including a novel stochastic algorithm and two top-down hierarchical classification methods for multi-label literature classification. We systematically evaluated and compared these graph-based classification algorithms to a conventional flat multi-label algorithm. The results indicate that, through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods can significantly improve predictions of the Gene Ontology terms implied by the analyzed text. Furthermore, the graph-based multi-label classifiers are capable of suggesting Gene Ontology annotations (to curators) that are closely related to the true annotations even if they fail to predict the true ones directly. A software package implementing the studied algorithms is available for the research community. Through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods have better potential than the conventional flat multi-label classification approach to facilitate protein annotation based on the literature.

Retina verification system based on biometric graph matching.

PubMed

Lajevardi, Seyed Mehdi; Arakala, Arathi; Davis, Stephen A; Horadam, Kathy J

2013-09-01

This paper presents an automatic retina verification framework based on the biometric graph matching (BGM) algorithm. The retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators. Then, retinal templates are defined as formal spatial graphs derived from the retinal vasculature. The BGM algorithm, a noisy graph matching algorithm, robust to translation, non-linear distortion, and small rotations, is used to compare retinal templates. The BGM algorithm uses graph topology to define three distance measures between a pair of graphs, two of which are new. A support vector machine (SVM) classifier is used to distinguish between genuine and imposter comparisons. Using single as well as multiple graph measures, the classifier achieves complete separation on a training set of images from the VARIA database (60% of the data), equaling the state-of-the-art for retina verification. Because the available data set is small, kernel density estimation (KDE) of the genuine and imposter score distributions of the training set are used to measure performance of the BGM algorithm. In the one dimensional case, the KDE model is validated with the testing set. A 0 EER on testing shows that the KDE model is a good fit for the empirical distribution. For the multiple graph measures, a novel combination of the SVM boundary and the KDE model is used to obtain a fair comparison with the KDE model for the single measure. A clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60% and more than two orders of magnitude.

Learning graph matching.

PubMed

Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J

2009-06-01

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

Hash Bit Selection for Nearest Neighbor Search.

PubMed

Xianglong Liu; Junfeng He; Shih-Fu Chang

2017-11-01

To overcome the barrier of storage and computation when dealing with gigantic-scale data sets, compact hashing has been studied extensively to approximate the nearest neighbor search. Despite the recent advances, critical design issues remain open in how to select the right features, hashing algorithms, and/or parameter settings. In this paper, we address these by posing an optimal hash bit selection problem, in which an optimal subset of hash bits are selected from a pool of candidate bits generated by different features, algorithms, or parameters. Inspired by the optimization criteria used in existing hashing algorithms, we adopt the bit reliability and their complementarity as the selection criteria that can be carefully tailored for hashing performance in different tasks. Then, the bit selection solution is discovered by finding the best tradeoff between search accuracy and time using a modified dynamic programming method. To further reduce the computational complexity, we employ the pairwise relationship among hash bits to approximate the high-order independence property, and formulate it as an efficient quadratic programming method that is theoretically equivalent to the normalized dominant set problem in a vertex- and edge-weighted graph. Extensive large-scale experiments have been conducted under several important application scenarios of hash techniques, where our bit selection framework can achieve superior performance over both the naive selection methods and the state-of-the-art hashing algorithms, with significant accuracy gains ranging from 10% to 50%, relatively.

Fat water decomposition using globally optimal surface estimation (GOOSE) algorithm.

PubMed

Cui, Chen; Wu, Xiaodong; Newell, John D; Jacob, Mathews

2015-03-01

This article focuses on developing a novel noniterative fat water decomposition algorithm more robust to fat water swaps and related ambiguities. Field map estimation is reformulated as a constrained surface estimation problem to exploit the spatial smoothness of the field, thus minimizing the ambiguities in the recovery. Specifically, the differences in the field map-induced frequency shift between adjacent voxels are constrained to be in a finite range. The discretization of the above problem yields a graph optimization scheme, where each node of the graph is only connected with few other nodes. Thanks to the low graph connectivity, the problem is solved efficiently using a noniterative graph cut algorithm. The global minimum of the constrained optimization problem is guaranteed. The performance of the algorithm is compared with that of state-of-the-art schemes. Quantitative comparisons are also made against reference data. The proposed algorithm is observed to yield more robust fat water estimates with fewer fat water swaps and better quantitative results than other state-of-the-art algorithms in a range of challenging applications. The proposed algorithm is capable of considerably reducing the swaps in challenging fat water decomposition problems. The experiments demonstrate the benefit of using explicit smoothness constraints in field map estimation and solving the problem using a globally convergent graph-cut optimization algorithm. © 2014 Wiley Periodicals, Inc.

Efficient solution for finding Hamilton cycles in undirected graphs.

PubMed

Alhalabi, Wadee; Kitanneh, Omar; Alharbi, Amira; Balfakih, Zain; Sarirete, Akila

2016-01-01

The Hamilton cycle problem is closely related to a series of famous problems and puzzles (traveling salesman problem, Icosian game) and, due to the fact that it is NP-complete, it was extensively studied with different algorithms to solve it. The most efficient algorithm is not known. In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many Hamiltonian and non-Hamiltonian graphs. This provides a new effective approach to solve a problem that is fundamental in graph theory and can influence the manner in which the existing applications are used and improved.

MoleculaRnetworks: an integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation.

PubMed

Mooney, Barbara Logan; Corrales, L René; Clark, Aurora E

2012-03-30

This work discusses scripts for processing molecular simulations data written using the software package R: A Language and Environment for Statistical Computing. These scripts, named moleculaRnetworks, are intended for the geometric and solvent network analysis of aqueous solutes and can be extended to other H-bonded solvents. New algorithms, several of which are based on graph theory, that interrogate the solvent environment about a solute are presented and described. This includes a novel method for identifying the geometric shape adopted by the solvent in the immediate vicinity of the solute and an exploratory approach for describing H-bonding, both based on the PageRank algorithm of Google search fame. The moleculaRnetworks codes include a preprocessor, which distills simulation trajectories into physicochemical data arrays, and an interactive analysis script that enables statistical, trend, and correlation analysis, and other data mining. The goal of these scripts is to increase access to the wealth of structural and dynamical information that can be obtained from molecular simulations. Copyright © 2012 Wiley Periodicals, Inc.

Application of kernel functions for accurate similarity search in large chemical databases.

PubMed

Wang, Xiaohong; Huan, Jun; Smalter, Aaron; Lushington, Gerald H

2010-04-29

Similarity search in chemical structure databases is an important problem with many applications in chemical genomics, drug design, and efficient chemical probe screening among others. It is widely believed that structure based methods provide an efficient way to do the query. Recently various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models, graph kernel functions can not be applied to large chemical compound database due to the high computational complexity and the difficulties in indexing similarity search for large databases. To bridge graph kernel function and similarity search in chemical databases, we applied a novel kernel-based similarity measurement, developed in our team, to measure similarity of graph represented chemicals. In our method, we utilize a hash table to support new graph kernel function definition, efficient storage and fast search. We have applied our method, named G-hash, to large chemical databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Moreover, the similarity measurement and the index structure is scalable to large chemical databases with smaller indexing size, and faster query processing time as compared to state-of-the-art indexing methods such as Daylight fingerprints, C-tree and GraphGrep. Efficient similarity query processing method for large chemical databases is challenging since we need to balance running time efficiency and similarity search accuracy. Our previous similarity search method, G-hash, provides a new way to perform similarity search in chemical databases. Experimental study validates the utility of G-hash in chemical databases.

Quantum speedup of the traveling-salesman problem for bounded-degree graphs

NASA Astrophysics Data System (ADS)

Moylett, Dominic J.; Linden, Noah; Montanaro, Ashley

2017-03-01

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

Linear Algebra and Sequential Importance Sampling for Network Reliability

DTIC Science & Technology

2011-12-01

first test case is an Erdős- Renyi graph with 100 vertices and 150 edges. Figure 1 depicts the relative variance of the three Algorithms: Algorithm TOP...e va ria nc e Figure 1: Relative variance of various algorithms on Erdős Renyi graph, 100 vertices 250 edges. Key: Solid = TOP-DOWN algorithm

PANDA: Protein function prediction using domain architecture and affinity propagation.

PubMed

Wang, Zheng; Zhao, Chenguang; Wang, Yiheng; Sun, Zheng; Wang, Nan

2018-02-22

We developed PANDA (Propagation of Affinity and Domain Architecture) to predict protein functions in the format of Gene Ontology (GO) terms. PANDA at first executes profile-profile alignment algorithm to search against PfamA, KOG, COG, and SwissProt databases, and then launches PSI-BLAST against UniProt for homologue search. PANDA integrates a domain architecture inference algorithm based on the Bayesian statistics that calculates the probability of having a GO term. All the candidate GO terms are pooled and filtered based on Z-score. After that, the remaining GO terms are clustered using an affinity propagation algorithm based on the GO directed acyclic graph, followed by a second round of filtering on the clusters of GO terms. We benchmarked the performance of all the baseline predictors PANDA integrates and also for every pooling and filtering step of PANDA. It can be found that PANDA achieves better performances in terms of area under the curve for precision and recall compared to the baseline predictors. PANDA can be accessed from http://dna.cs.miami.edu/PANDA/ .

Visual graph query formulation and exploration: a new perspective on information retrieval at the edge

NASA Astrophysics Data System (ADS)

Kase, Sue E.; Vanni, Michelle; Knight, Joanne A.; Su, Yu; Yan, Xifeng

2016-05-01

Within operational environments decisions must be made quickly based on the information available. Identifying an appropriate knowledge base and accurately formulating a search query are critical tasks for decision-making effectiveness in dynamic situations. The spreading of graph data management tools to access large graph databases is a rapidly emerging research area of potential benefit to the intelligence community. A graph representation provides a natural way of modeling data in a wide variety of domains. Graph structures use nodes, edges, and properties to represent and store data. This research investigates the advantages of information search by graph query initiated by the analyst and interactively refined within the contextual dimensions of the answer space toward a solution. The paper introduces SLQ, a user-friendly graph querying system enabling the visual formulation of schemaless and structureless graph queries. SLQ is demonstrated with an intelligence analyst information search scenario focused on identifying individuals responsible for manufacturing a mosquito-hosted deadly virus. The scenario highlights the interactive construction of graph queries without prior training in complex query languages or graph databases, intuitive navigation through the problem space, and visualization of results in graphical format.

Mining connected global and local dense subgraphs for bigdata

NASA Astrophysics Data System (ADS)

Wu, Bo; Shen, Haiying

2016-01-01

The problem of discovering connected dense subgraphs of natural graphs is important in data analysis. Discovering dense subgraphs that do not contain denser subgraphs or are not contained in denser subgraphs (called significant dense subgraphs) is also critical for wide-ranging applications. In spite of many works on discovering dense subgraphs, there are no algorithms that can guarantee the connectivity of the returned subgraphs or discover significant dense subgraphs. Hence, in this paper, we define two subgraph discovery problems to discover connected and significant dense subgraphs, propose polynomial-time algorithms and theoretically prove their validity. We also propose an algorithm to further improve the time and space efficiency of our basic algorithm for discovering significant dense subgraphs in big data by taking advantage of the unique features of large natural graphs. In the experiments, we use massive natural graphs to evaluate our algorithms in comparison with previous algorithms. The experimental results show the effectiveness of our algorithms for the two problems and their efficiency. This work is also the first that reveals the physical significance of significant dense subgraphs in natural graphs from different domains.

Integrated scheduling of a container handling system with simultaneous loading and discharging operations

NASA Astrophysics Data System (ADS)

Li, Chen; Lu, Zhiqiang; Han, Xiaole; Zhang, Yuejun; Wang, Li

2016-03-01

The integrated scheduling of container handling systems aims to optimize the coordination and overall utilization of all handling equipment, so as to minimize the makespan of a given set of container tasks. A modified disjunctive graph is proposed and a mixed 0-1 programming model is formulated. A heuristic algorithm is presented, in which the original problem is divided into two subproblems. In the first subproblem, contiguous bay crane operations are applied to obtain a good quay crane schedule. In the second subproblem, proper internal truck and yard crane schedules are generated to match the given quay crane schedule. Furthermore, a genetic algorithm based on the heuristic algorithm is developed to search for better solutions. The computational results show that the proposed algorithm can efficiently find high-quality solutions. They also indicate the effectiveness of simultaneous loading and discharging operations compared with separate ones.

Exact analytical solution of irreversible binary dynamics on networks.

PubMed

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Exact analytical solution of irreversible binary dynamics on networks

NASA Astrophysics Data System (ADS)

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J.

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Mathematical foundations of the GraphBLAS

DOE PAGES

Kepner, Jeremy; Aaltonen, Peter; Bader, David; ...

2016-12-01

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, themore » two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.« less

A Statistical Method to Distinguish Functional Brain Networks

PubMed Central

Fujita, André; Vidal, Maciel C.; Takahashi, Daniel Y.

2017-01-01

One major problem in neuroscience is the comparison of functional brain networks of different populations, e.g., distinguishing the networks of controls and patients. Traditional algorithms are based on search for isomorphism between networks, assuming that they are deterministic. However, biological networks present randomness that cannot be well modeled by those algorithms. For instance, functional brain networks of distinct subjects of the same population can be different due to individual characteristics. Moreover, networks of subjects from different populations can be generated through the same stochastic process. Thus, a better hypothesis is that networks are generated by random processes. In this case, subjects from the same group are samples from the same random process, whereas subjects from different groups are generated by distinct processes. Using this idea, we developed a statistical test called ANOGVA to test whether two or more populations of graphs are generated by the same random graph model. Our simulations' results demonstrate that we can precisely control the rate of false positives and that the test is powerful to discriminate random graphs generated by different models and parameters. The method also showed to be robust for unbalanced data. As an example, we applied ANOGVA to an fMRI dataset composed of controls and patients diagnosed with autism or Asperger. ANOGVA identified the cerebellar functional sub-network as statistically different between controls and autism (p < 0.001). PMID:28261045

A Statistical Method to Distinguish Functional Brain Networks.

PubMed

Fujita, André; Vidal, Maciel C; Takahashi, Daniel Y

2017-01-01

One major problem in neuroscience is the comparison of functional brain networks of different populations, e.g., distinguishing the networks of controls and patients. Traditional algorithms are based on search for isomorphism between networks, assuming that they are deterministic. However, biological networks present randomness that cannot be well modeled by those algorithms. For instance, functional brain networks of distinct subjects of the same population can be different due to individual characteristics. Moreover, networks of subjects from different populations can be generated through the same stochastic process. Thus, a better hypothesis is that networks are generated by random processes. In this case, subjects from the same group are samples from the same random process, whereas subjects from different groups are generated by distinct processes. Using this idea, we developed a statistical test called ANOGVA to test whether two or more populations of graphs are generated by the same random graph model. Our simulations' results demonstrate that we can precisely control the rate of false positives and that the test is powerful to discriminate random graphs generated by different models and parameters. The method also showed to be robust for unbalanced data. As an example, we applied ANOGVA to an fMRI dataset composed of controls and patients diagnosed with autism or Asperger. ANOGVA identified the cerebellar functional sub-network as statistically different between controls and autism ( p < 0.001).

Computing Strongly Connected Components in the Streaming Model

NASA Astrophysics Data System (ADS)

Laura, Luigi; Santaroni, Federico

In this paper we present the first algorithm to compute the Strongly Connected Components of a graph in the datastream model (W-Stream), where the graph is represented by a stream of edges and we are allowed to produce intermediate output streams. The algorithm is simple, effective, and can be implemented with few lines of code: it looks at each edge in the stream, and selects the appropriate action with respect to a tree T, representing the graph connectivity seen so far. We analyze the theoretical properties of the algorithm: correctness, memory occupation (O(n logn)), per item processing time (bounded by the current height of T), and number of passes (bounded by the maximal height of T). We conclude by presenting a brief experimental evaluation of the algorithm against massive synthetic and real graphs that confirms its effectiveness: with graphs with up to 100M nodes and 4G edges, only few passes are needed, and millions of edges per second are processed.

Property Graph vs RDF Triple Store: A Comparison on Glycan Substructure Search

PubMed Central

Alocci, Davide; Mariethoz, Julien; Horlacher, Oliver; Bolleman, Jerven T.; Campbell, Matthew P.; Lisacek, Frederique

2015-01-01

Resource description framework (RDF) and Property Graph databases are emerging technologies that are used for storing graph-structured data. We compare these technologies through a molecular biology use case: glycan substructure search. Glycans are branched tree-like molecules composed of building blocks linked together by chemical bonds. The molecular structure of a glycan can be encoded into a direct acyclic graph where each node represents a building block and each edge serves as a chemical linkage between two building blocks. In this context, Graph databases are possible software solutions for storing glycan structures and Graph query languages, such as SPARQL and Cypher, can be used to perform a substructure search. Glycan substructure searching is an important feature for querying structure and experimental glycan databases and retrieving biologically meaningful data. This applies for example to identifying a region of the glycan recognised by a glycan binding protein (GBP). In this study, 19,404 glycan structures were selected from GlycomeDB (www.glycome-db.org) and modelled for being stored into a RDF triple store and a Property Graph. We then performed two different sets of searches and compared the query response times and the results from both technologies to assess performance and accuracy. The two implementations produced the same results, but interestingly we noted a difference in the query response times. Qualitative measures such as portability were also used to define further criteria for choosing the technology adapted to solving glycan substructure search and other comparable issues. PMID:26656740

ActiviTree: interactive visual exploration of sequences in event-based data using graph similarity.

PubMed

Vrotsou, Katerina; Johansson, Jimmy; Cooper, Matthew

2009-01-01

The identification of significant sequences in large and complex event-based temporal data is a challenging problem with applications in many areas of today's information intensive society. Pure visual representations can be used for the analysis, but are constrained to small data sets. Algorithmic search mechanisms used for larger data sets become expensive as the data size increases and typically focus on frequency of occurrence to reduce the computational complexity, often overlooking important infrequent sequences and outliers. In this paper we introduce an interactive visual data mining approach based on an adaptation of techniques developed for web searching, combined with an intuitive visual interface, to facilitate user-centred exploration of the data and identification of sequences significant to that user. The search algorithm used in the exploration executes in negligible time, even for large data, and so no pre-processing of the selected data is required, making this a completely interactive experience for the user. Our particular application area is social science diary data but the technique is applicable across many other disciplines.

Indexing Volumetric Shapes with Matching and Packing

PubMed Central

Koes, David Ryan; Camacho, Carlos J.

2014-01-01

We describe a novel algorithm for bulk-loading an index with high-dimensional data and apply it to the problem of volumetric shape matching. Our matching and packing algorithm is a general approach for packing data according to a similarity metric. First an approximate k-nearest neighbor graph is constructed using vantage-point initialization, an improvement to previous work that decreases construction time while improving the quality of approximation. Then graph matching is iteratively performed to pack related items closely together. The end result is a dense index with good performance. We define a new query specification for shape matching that uses minimum and maximum shape constraints to explicitly specify the spatial requirements of the desired shape. This specification provides a natural language for performing volumetric shape matching and is readily supported by the geometry-based similarity search (GSS) tree, an indexing structure that maintains explicit representations of volumetric shape. We describe our implementation of a GSS tree for volumetric shape matching and provide a comprehensive evaluation of parameter sensitivity, performance, and scalability. Compared to previous bulk-loading algorithms, we find that matching and packing can construct a GSS-tree index in the same amount of time that is denser, flatter, and better performing, with an observed average performance improvement of 2X. PMID:26085707

Efficient searching and annotation of metabolic networks using chemical similarity

PubMed Central

Pertusi, Dante A.; Stine, Andrew E.; Broadbelt, Linda J.; Tyo, Keith E.J.

2015-01-01

Motivation: The urgent need for efficient and sustainable biological production of fuels and high-value chemicals has elicited a wave of in silico techniques for identifying promising novel pathways to these compounds in large putative metabolic networks. To date, these approaches have primarily used general graph search algorithms, which are prohibitively slow as putative metabolic networks may exceed 1 million compounds. To alleviate this limitation, we report two methods—SimIndex (SI) and SimZyme—which use chemical similarity of 2D chemical fingerprints to efficiently navigate large metabolic networks and propose enzymatic connections between the constituent nodes. We also report a Byers–Waterman type pathway search algorithm for further paring down pertinent networks. Results: Benchmarking tests run with SI show it can reduce the number of nodes visited in searching a putative network by 100-fold with a computational time improvement of up to 105-fold. Subsequent Byers–Waterman search application further reduces the number of nodes searched by up to 100-fold, while SimZyme demonstrates ∼90% accuracy in matching query substrates with enzymes. Using these modules, we have designed and annotated an alternative to the methylerythritol phosphate pathway to produce isopentenyl pyrophosphate with more favorable thermodynamics than the native pathway. These algorithms will have a significant impact on our ability to use large metabolic networks that lack annotation of promiscuous reactions. Availability and implementation: Python files will be available for download at http://tyolab.northwestern.edu/tools/. Contact: k-tyo@northwestern.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25417203

Efficient searching and annotation of metabolic networks using chemical similarity.

PubMed

Pertusi, Dante A; Stine, Andrew E; Broadbelt, Linda J; Tyo, Keith E J

2015-04-01

The urgent need for efficient and sustainable biological production of fuels and high-value chemicals has elicited a wave of in silico techniques for identifying promising novel pathways to these compounds in large putative metabolic networks. To date, these approaches have primarily used general graph search algorithms, which are prohibitively slow as putative metabolic networks may exceed 1 million compounds. To alleviate this limitation, we report two methods--SimIndex (SI) and SimZyme--which use chemical similarity of 2D chemical fingerprints to efficiently navigate large metabolic networks and propose enzymatic connections between the constituent nodes. We also report a Byers-Waterman type pathway search algorithm for further paring down pertinent networks. Benchmarking tests run with SI show it can reduce the number of nodes visited in searching a putative network by 100-fold with a computational time improvement of up to 10(5)-fold. Subsequent Byers-Waterman search application further reduces the number of nodes searched by up to 100-fold, while SimZyme demonstrates ∼ 90% accuracy in matching query substrates with enzymes. Using these modules, we have designed and annotated an alternative to the methylerythritol phosphate pathway to produce isopentenyl pyrophosphate with more favorable thermodynamics than the native pathway. These algorithms will have a significant impact on our ability to use large metabolic networks that lack annotation of promiscuous reactions. Python files will be available for download at http://tyolab.northwestern.edu/tools/. Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

An algorithm for automatic reduction of complex signal flow graphs

NASA Technical Reports Server (NTRS)

Young, K. R.; Hoberock, L. L.; Thompson, J. G.

1976-01-01

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm

NASA Astrophysics Data System (ADS)

Liang, Yufeng; Prendergast, David

2018-05-01

The growing interest in using x-ray spectroscopy for refined materials characterization calls for an accurate electronic-structure theory to interpret the x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a nondiagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017), 10.1103/PhysRevLett.118.096402], we exploit the linear dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of vanishingly small terms. This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path-finding process. We demonstrate that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.

Semantic Drift in Espresso-style Bootstrapping: Graph-theoretic Analysis and Evaluation in Word Sense Disambiguation

NASA Astrophysics Data System (ADS)

Komachi, Mamoru; Kudo, Taku; Shimbo, Masashi; Matsumoto, Yuji

Bootstrapping has a tendency, called semantic drift, to select instances unrelated to the seed instances as the iteration proceeds. We demonstrate the semantic drift of Espresso-style bootstrapping has the same root as the topic drift of Kleinberg's HITS, using a simplified graph-based reformulation of bootstrapping. We confirm that two graph-based algorithms, the von Neumann kernels and the regularized Laplacian, can reduce the effect of semantic drift in the task of word sense disambiguation (WSD) on Senseval-3 English Lexical Sample Task. Proposed algorithms achieve superior performance to Espresso and previous graph-based WSD methods, even though the proposed algorithms have less parameters and are easy to calibrate.

Parallel algorithms for the molecular conformation problem

NASA Astrophysics Data System (ADS)

Rajan, Kumar

Given a set of objects, and some of the pairwise distances between them, the problem of identifying the positions of the objects in the Euclidean space is referred to as the molecular conformation problem. This problem is known to be computationally difficult. One of the most important applications of this problem is the determination of the structure of molecules. In the case of molecular structure determination, usually only the lower and upper bounds on some of the interatomic distances are available. The process of obtaining a tighter set of bounds between all pairs of atoms, using the available interatomic distance bounds is referred to as bound-smoothing . One method for bound-smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality---the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley-Menger determinants. The sequential tetrangle-inequality bound-smoothing algorithm considers a quadruple of atoms at a time, and tightens the bounds on each of its six distances. The sequential algorithm is computationally expensive, and its application is limited to molecules with up to a few hundred atoms. Here, we conduct an experimental study of tetrangle-inequality bound-smoothing and reduce the sequential time by identifying the most computationally expensive portions of the process. We also present a simple criterion to determine which of the quadruples of atoms are likely to be tightened the most by tetrangle-inequality bound-smoothing. This test could be used to enhance the applicability of this process to large molecules. We map the problem of parallelizing tetrangle-inequality bound-smoothing to that of generating disjoint packing designs of a certain kind. We map this, in turn, to a regular-graph coloring problem, and present a simple, parallel algorithm for tetrangle-inequality bound-smoothing. We implement the parallel algorithm on the Intel Paragon X/PS, and apply it to real-life molecules. Our results show that with this parallel algorithm, tetrangle inequality can be applied to large molecules in a reasonable amount of time. We extend the regular graph to represent more general packing designs, and present a coloring algorithm for this graph. This can be used to generate constant-weight binary codes in parallel. Once a tighter set of distance bounds is obtained, the molecular conformation problem is usually formulated as a non-linear optimization problem, and a global optimization algorithm is then used to solve the problem. Here we present a parallel, deterministic algorithm for the optimization problem based on Interval Analysis. We implement our algorithm, using dynamic load balancing, on a network of Sun Ultra-Sparc workstations. Our experience with this algorithm shows that its application is limited to small instances of the molecular conformation problem, where the number of measured, pairwise distances is close to the maximum value. However, since the interval method eliminates a substantial portion of the initial search space very quickly, it can be used to prune the search space before any of the more efficient, nondeterministic methods can be applied.

An efficient algorithm for pairwise local alignment of protein interaction networks

DOE PAGES

Chen, Wenbin; Schmidt, Matthew; Tian, Wenhong; ...

2015-04-01

Recently, researchers seeking to understand, modify, and create beneficial traits in organisms have looked for evolutionarily conserved patterns of protein interactions. Their conservation likely means that the proteins of these conserved functional modules are important to the trait's expression. In this paper, we formulate the problem of identifying these conserved patterns as a graph optimization problem, and develop a fast heuristic algorithm for this problem. We compare the performance of our network alignment algorithm to that of the MaWISh algorithm [Koyuturk M, Kim Y, Topkara U, Subramaniam S, Szpankowski W, Grama A, Pairwise alignment of protein interaction networks, J Computmore » Biol 13(2): 182-199, 2006.], which bases its search algorithm on a related decision problem formulation. We find that our algorithm discovers conserved modules with a larger number of proteins in an order of magnitude less time. In conclusion, the protein sets found by our algorithm correspond to known conserved functional modules at comparable precision and recall rates as those produced by the MaWISh algorithm.« less

Semantic super networks: A case analysis of Wikipedia papers

NASA Astrophysics Data System (ADS)

Kostyuchenko, Evgeny; Lebedeva, Taisiya; Goritov, Alexander

2017-11-01

An algorithm for constructing super-large semantic networks has been developed in current work. Algorithm was tested using the "Cosmos" category of the Internet encyclopedia "Wikipedia" as an example. During the implementation, a parser for the syntax analysis of Wikipedia pages was developed. A graph based on list of articles and categories was formed. On the basis of the obtained graph analysis, algorithms for finding domains of high connectivity in a graph were proposed and tested. Algorithms for constructing a domain based on the number of links and the number of articles in the current subject area is considered. The shortcomings of these algorithms are shown and explained, an algorithm is developed on their joint use. The possibility of applying a combined algorithm for obtaining the final domain is shown. The problem of instability of the received domain was discovered when starting an algorithm from two neighboring vertices related to the domain.

Overlapping community detection based on link graph using distance dynamics

NASA Astrophysics Data System (ADS)

Chen, Lei; Zhang, Jing; Cai, Li-Jun

2018-01-01

The distance dynamics model was recently proposed to detect the disjoint community of a complex network. To identify the overlapping structure of a network using the distance dynamics model, an overlapping community detection algorithm, called L-Attractor, is proposed in this paper. The process of L-Attractor mainly consists of three phases. In the first phase, L-Attractor transforms the original graph to a link graph (a new edge graph) to assure that one node has multiple distances. In the second phase, using the improved distance dynamics model, a dynamic interaction process is introduced to simulate the distance dynamics (shrink or stretch). Through the dynamic interaction process, all distances converge, and the disjoint community structure of the link graph naturally manifests itself. In the third phase, a recovery method is designed to convert the disjoint community structure of the link graph to the overlapping community structure of the original graph. Extensive experiments are conducted on the LFR benchmark networks as well as real-world networks. Based on the results, our algorithm demonstrates higher accuracy and quality than other state-of-the-art algorithms.

Properties of heuristic search strategies

NASA Technical Reports Server (NTRS)

Vanderbrug, G. J.

1973-01-01

A directed graph is used to model the search space of a state space representation with single input operators, an AND/OR is used for problem reduction representations, and a theorem proving graph is used for state space representations with multiple input operators. These three graph models and heuristic strategies for searching them are surveyed. The completeness, admissibility, and optimality properties of search strategies which use the evaluation function f = (1 - omega)g = omega(h) are presented and interpreted using a representation of the search process in the plane. The use of multiple output operators to imply dependent successors, and thus obtain a formalism which includes all three types of representations, is discussed.

Path Planning for Non-Circular, Non-Holonomic Robots in Highly Cluttered Environments.

PubMed

Samaniego, Ricardo; Lopez, Joaquin; Vazquez, Fernando

2017-08-15

This paper presents an algorithm for finding a solution to the problem of planning a feasible path for a slender autonomous mobile robot in a large and cluttered environment. The presented approach is based on performing a graph search on a kinodynamic-feasible lattice state space of high resolution; however, the technique is applicable to many search algorithms. With the purpose of allowing the algorithm to consider paths that take the robot through narrow passes and close to obstacles, high resolutions are used for the lattice space and the control set. This introduces new challenges because one of the most computationally expensive parts of path search based planning algorithms is calculating the cost of each one of the actions or steps that could potentially be part of the trajectory. The reason for this is that the evaluation of each one of these actions involves convolving the robot's footprint with a portion of a local map to evaluate the possibility of a collision, an operation that grows exponentially as the resolution is increased. The novel approach presented here reduces the need for these convolutions by using a set of offline precomputed maps that are updated, by means of a partial convolution, as new information arrives from sensors or other sources. Not only does this improve run-time performance, but it also provides support for dynamic search in changing environments. A set of alternative fast convolution methods are also proposed, depending on whether the environment is cluttered with obstacles or not. Finally, we provide both theoretical and experimental results from different experiments and applications.

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

NASA Astrophysics Data System (ADS)

Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán

2016-07-01

We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation problem. The general version of the algorithm is presented and analyzed.

An efficient and scalable graph modeling approach for capturing information at different levels in next generation sequencing reads

PubMed Central

2013-01-01

Background Next generation sequencing technologies have greatly advanced many research areas of the biomedical sciences through their capability to generate massive amounts of genetic information at unprecedented rates. The advent of next generation sequencing has led to the development of numerous computational tools to analyze and assemble the millions to billions of short sequencing reads produced by these technologies. While these tools filled an important gap, current approaches for storing, processing, and analyzing short read datasets generally have remained simple and lack the complexity needed to efficiently model the produced reads and assemble them correctly. Results Previously, we presented an overlap graph coarsening scheme for modeling read overlap relationships on multiple levels. Most current read assembly and analysis approaches use a single graph or set of clusters to represent the relationships among a read dataset. Instead, we use a series of graphs to represent the reads and their overlap relationships across a spectrum of information granularity. At each information level our algorithm is capable of generating clusters of reads from the reduced graph, forming an integrated graph modeling and clustering approach for read analysis and assembly. Previously we applied our algorithm to simulated and real 454 datasets to assess its ability to efficiently model and cluster next generation sequencing data. In this paper we extend our algorithm to large simulated and real Illumina datasets to demonstrate that our algorithm is practical for both sequencing technologies. Conclusions Our overlap graph theoretic algorithm is able to model next generation sequencing reads at various levels of granularity through the process of graph coarsening. Additionally, our model allows for efficient representation of the read overlap relationships, is scalable for large datasets, and is practical for both Illumina and 454 sequencing technologies. PMID:24564333

Model of twelve properties of a set of organic solvents with graph-theoretical and/or experimental parameters.

PubMed

Pogliani, Lionello

2010-01-30

Twelve properties of a highly heterogeneous class of organic solvents have been modeled with a graph-theoretical molecular connectivity modified (MC) method, which allows to encode the core electrons and the hydrogen atoms. The graph-theoretical method uses the concepts of simple, general, and complete graphs, where these last types of graphs are used to encode the core electrons. The hydrogen atoms have been encoded by the aid of a graph-theoretical perturbation parameter, which contributes to the definition of the valence delta, delta(v), a key parameter in molecular connectivity studies. The model of the twelve properties done with a stepwise search algorithm is always satisfactory, and it allows to check the influence of the hydrogen content of the solvent molecules on the choice of the type of descriptor. A similar argument holds for the influence of the halogen atoms on the type of core electron representation. In some cases the molar mass, and in a minor way, special "ad hoc" parameters have been used to improve the model. A very good model of the surface tension could be obtained by the aid of five experimental parameters. A mixed model method based on experimental parameters plus molecular connectivity indices achieved, instead, to consistently improve the model quality of five properties. To underline is the importance of the boiling point temperatures as descriptors in these last two model methodologies. Copyright 2009 Wiley Periodicals, Inc.

An intelligent allocation algorithm for parallel processing

NASA Technical Reports Server (NTRS)

Carroll, Chester C.; Homaifar, Abdollah; Ananthram, Kishan G.

1988-01-01

The problem of allocating nodes of a program graph to processors in a parallel processing architecture is considered. The algorithm is based on critical path analysis, some allocation heuristics, and the execution granularity of nodes in a program graph. These factors, and the structure of interprocessor communication network, influence the allocation. To achieve realistic estimations of the executive durations of allocations, the algorithm considers the fact that nodes in a program graph have to communicate through varying numbers of tokens. Coarse and fine granularities have been implemented, with interprocessor token-communication duration, varying from zero up to values comparable to the execution durations of individual nodes. The effect on allocation of communication network structures is demonstrated by performing allocations for crossbar (non-blocking) and star (blocking) networks. The algorithm assumes the availability of as many processors as it needs for the optimal allocation of any program graph. Hence, the focus of allocation has been on varying token-communication durations rather than varying the number of processors. The algorithm always utilizes as many processors as necessary for the optimal allocation of any program graph, depending upon granularity and characteristics of the interprocessor communication network.

GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith

2014-08-25

Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines themore » scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.« less

Scalable Triadic Analysis of Large-Scale Graphs: Multi-Core vs. Multi-Processor vs. Multi-Threaded Shared Memory Architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chin, George; Marquez, Andres; Choudhury, Sutanay

2012-09-01

Triadic analysis encompasses a useful set of graph mining methods that is centered on the concept of a triad, which is a subgraph of three nodes and the configuration of directed edges across the nodes. Such methods are often applied in the social sciences as well as many other diverse fields. Triadic methods commonly operate on a triad census that counts the number of triads of every possible edge configuration in a graph. Like other graph algorithms, triadic census algorithms do not scale well when graphs reach tens of millions to billions of nodes. To enable the triadic analysis ofmore » large-scale graphs, we developed and optimized a triad census algorithm to efficiently execute on shared memory architectures. We will retrace the development and evolution of a parallel triad census algorithm. Over the course of several versions, we continually adapted the code’s data structures and program logic to expose more opportunities to exploit parallelism on shared memory that would translate into improved computational performance. We will recall the critical steps and modifications that occurred during code development and optimization. Furthermore, we will compare the performances of triad census algorithm versions on three specific systems: Cray XMT, HP Superdome, and AMD multi-core NUMA machine. These three systems have shared memory architectures but with markedly different hardware capabilities to manage parallelism.« less

Geographic Gossip: Efficient Averaging for Sensor Networks

NASA Astrophysics Data System (ADS)

Dimakis, Alexandros D. G.; Sarwate, Anand D.; Wainwright, Martin J.

Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of $n$ and $\\sqrt{n}$ respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy $\\epsilon$ using $O(\\frac{n^{1.5}}{\\sqrt{\\log n}} \\log \\epsilon^{-1})$ radio transmissions, which yields a $\\sqrt{\\frac{n}{\\log n}}$ factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.

Parallel approach on sorting of genes in search of optimal solution.

PubMed

Kumar, Pranav; Sahoo, G

2018-05-01

An important tool for comparing genome analysis is the rearrangement event that can transform one given genome into other. For finding minimum sequence of fission and fusion, we have proposed here an algorithm and have shown a transformation example for converting the source genome into the target genome. The proposed algorithm comprises of circular sequence i.e. "cycle graph" in place of mapping. The main concept of algorithm is based on optimal result of permutation. These sorting processes are performed in constant running time by showing permutation in the form of cycle. In biological instances it has been observed that transposition occurs half of the frequency as that of reversal. In this paper we are not dealing with reversal instead commencing with the rearrangement of fission, fusion as well as transposition. Copyright © 2017 Elsevier Inc. All rights reserved.

Left-ventricle segmentation in real-time 3D echocardiography using a hybrid active shape model and optimal graph search approach

NASA Astrophysics Data System (ADS)

Zhang, Honghai; Abiose, Ademola K.; Campbell, Dwayne N.; Sonka, Milan; Martins, James B.; Wahle, Andreas

2010-03-01

Quantitative analysis of the left ventricular shape and motion patterns associated with left ventricular mechanical dyssynchrony (LVMD) is essential for diagnosis and treatment planning in congestive heart failure. Real-time 3D echocardiography (RT3DE) used for LVMD analysis is frequently limited by heavy speckle noise or partially incomplete data, thus a segmentation method utilizing learned global shape knowledge is beneficial. In this study, the endocardial surface of the left ventricle (LV) is segmented using a hybrid approach combining active shape model (ASM) with optimal graph search. The latter is used to achieve landmark refinement in the ASM framework. Optimal graph search translates the 3D segmentation into the detection of a minimum-cost closed set in a graph and can produce a globally optimal result. Various information-gradient, intensity distributions, and regional-property terms-are used to define the costs for the graph search. The developed method was tested on 44 RT3DE datasets acquired from 26 LVMD patients. The segmentation accuracy was assessed by surface positioning error and volume overlap measured for the whole LV as well as 16 standard LV regions. The segmentation produced very good results that were not achievable using ASM or graph search alone.

Connectivity: Performance Portable Algorithms for graph connectivity v. 0.1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slota, George; Rajamanickam, Sivasankaran; Madduri, Kamesh

Graphs occur in several places in real world from road networks, social networks and scientific simulations. Connectivity is a graph analysis software to graph connectivity in modern architectures like multicore CPUs, Xeon Phi and GPUs.

Combinatorial Algorithms to Enable Computational Science and Engineering: Work from the CSCAPES Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boman, Erik G.; Catalyurek, Umit V.; Chevalier, Cedric

2015-01-16

This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hypergraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellowsmore » have joined DOE Labs (Sandia, Berkeley), as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.« less

GraDit: graph-based data repair algorithm for multiple data edits rule violations

NASA Astrophysics Data System (ADS)

Ode Zuhayeni Madjida, Wa; Gusti Bagus Baskara Nugraha, I.

2018-03-01

Constraint-based data cleaning captures data violation to a set of rule called data quality rules. The rules consist of integrity constraint and data edits. Structurally, they are similar, where the rule contain left hand side and right hand side. Previous research proposed a data repair algorithm for integrity constraint violation. The algorithm uses undirected hypergraph as rule violation representation. Nevertheless, this algorithm can not be applied for data edits because of different rule characteristics. This study proposed GraDit, a repair algorithm for data edits rule. First, we use bipartite-directed hypergraph as model representation of overall defined rules. These representation is used for getting interaction between violation rules and clean rules. On the other hand, we proposed undirected graph as violation representation. Our experimental study showed that algorithm with undirected graph as violation representation model gave better data quality than algorithm with undirected hypergraph as representation model.

Direction of Auditory Pitch-Change Influences Visual Search for Slope From Graphs.

PubMed

Parrott, Stacey; Guzman-Martinez, Emmanuel; Orte, Laura; Grabowecky, Marcia; Huntington, Mark D; Suzuki, Satoru

2015-01-01

Linear trend (slope) is important information conveyed by graphs. We investigated how sounds influenced slope detection in a visual search paradigm. Four bar graphs or scatter plots were presented on each trial. Participants looked for a positive-slope or a negative-slope target (in blocked trials), and responded to targets in a go or no-go fashion. For example, in a positive-slope-target block, the target graph displayed a positive slope while other graphs displayed negative slopes (a go trial), or all graphs displayed negative slopes (a no-go trial). When an ascending or descending sound was presented concurrently, ascending sounds slowed detection of negative-slope targets whereas descending sounds slowed detection of positive-slope targets. The sounds had no effect when they immediately preceded the visual search displays, suggesting that the results were due to crossmodal interaction rather than priming. The sounds also had no effect when targets were words describing slopes, such as "positive," "negative," "increasing," or "decreasing," suggesting that the results were unlikely due to semantic-level interactions. Manipulations of spatiotemporal similarity between sounds and graphs had little effect. These results suggest that ascending and descending sounds influence visual search for slope based on a general association between the direction of auditory pitch-change and visual linear trend.

A sampling algorithm for segregation analysis

PubMed Central

Tier, Bruce; Henshall, John

2001-01-01

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated. PMID:11742631

Constructing Dense Graphs with Unique Hamiltonian Cycles

ERIC Educational Resources Information Center

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Xuanhua; Luo, Xuan; Liang, Junling

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weightmore » asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.« less

Geospatial-temporal semantic graph representations of trajectories from remote sensing and geolocation data

DOEpatents

Perkins, David Nikolaus; Brost, Randolph; Ray, Lawrence P.

2017-08-08

Various technologies for facilitating analysis of large remote sensing and geolocation datasets to identify features of interest are described herein. A search query can be submitted to a computing system that executes searches over a geospatial temporal semantic (GTS) graph to identify features of interest. The GTS graph comprises nodes corresponding to objects described in the remote sensing and geolocation datasets, and edges that indicate geospatial or temporal relationships between pairs of nodes in the nodes. Trajectory information is encoded in the GTS graph by the inclusion of movable nodes to facilitate searches for features of interest in the datasets relative to moving objects such as vehicles.

Statistically significant relational data mining :

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berry, Jonathan W.; Leung, Vitus Joseph; Phillips, Cynthia Ann

This report summarizes the work performed under the project (3z(BStatitically significant relational data mining.(3y (BThe goal of the project was to add more statistical rigor to the fairly ad hoc area of data mining on graphs. Our goal was to develop better algorithms and better ways to evaluate algorithm quality. We concetrated on algorithms for community detection, approximate pattern matching, and graph similarity measures. Approximate pattern matching involves finding an instance of a relatively small pattern, expressed with tolerance, in a large graph of data observed with uncertainty. This report gathers the abstracts and references for the eight refereed publicationsmore » that have appeared as part of this work. We then archive three pieces of research that have not yet been published. The first is theoretical and experimental evidence that a popular statistical measure for comparison of community assignments favors over-resolved communities over approximations to a ground truth. The second are statistically motivated methods for measuring the quality of an approximate match of a small pattern in a large graph. The third is a new probabilistic random graph model. Statisticians favor these models for graph analysis. The new local structure graph model overcomes some of the issues with popular models such as exponential random graph models and latent variable models.« less

Graphical Language for Data Processing

NASA Technical Reports Server (NTRS)

Alphonso, Keith

2011-01-01

A graphical language for processing data allows processing elements to be connected with virtual wires that represent data flows between processing modules. The processing of complex data, such as lidar data, requires many different algorithms to be applied. The purpose of this innovation is to automate the processing of complex data, such as LIDAR, without the need for complex scripting and programming languages. The system consists of a set of user-interface components that allow the user to drag and drop various algorithmic and processing components onto a process graph. By working graphically, the user can completely visualize the process flow and create complex diagrams. This innovation supports the nesting of graphs, such that a graph can be included in another graph as a single step for processing. In addition to the user interface components, the system includes a set of .NET classes that represent the graph internally. These classes provide the internal system representation of the graphical user interface. The system includes a graph execution component that reads the internal representation of the graph (as described above) and executes that graph. The execution of the graph follows the interpreted model of execution in that each node is traversed and executed from the original internal representation. In addition, there are components that allow external code elements, such as algorithms, to be easily integrated into the system, thus making the system infinitely expandable.

RAG-3D: A search tool for RNA 3D substructures

DOE PAGES

Zahran, Mai; Sevim Bayrak, Cigdem; Elmetwaly, Shereef; ...

2015-08-24

In this study, to address many challenges in RNA structure/function prediction, the characterization of RNA's modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally describedmore » in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.« less

RAG-3D: a search tool for RNA 3D substructures

PubMed Central

Zahran, Mai; Sevim Bayrak, Cigdem; Elmetwaly, Shereef; Schlick, Tamar

2015-01-01

To address many challenges in RNA structure/function prediction, the characterization of RNA's modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding. PMID:26304547

RAG-3D: A search tool for RNA 3D substructures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zahran, Mai; Sevim Bayrak, Cigdem; Elmetwaly, Shereef

In this study, to address many challenges in RNA structure/function prediction, the characterization of RNA's modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally describedmore » in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.« less

Survey of gene splicing algorithms based on reads.

PubMed

Si, Xiuhua; Wang, Qian; Zhang, Lei; Wu, Ruo; Ma, Jiquan

2017-11-02

Gene splicing is the process of assembling a large number of unordered short sequence fragments to the original genome sequence as accurately as possible. Several popular splicing algorithms based on reads are reviewed in this article, including reference genome algorithms and de novo splicing algorithms (Greedy-extension, Overlap-Layout-Consensus graph, De Bruijn graph). We also discuss a new splicing method based on the MapReduce strategy and Hadoop. By comparing these algorithms, some conclusions are drawn and some suggestions on gene splicing research are made.

Lifted worm algorithm for the Ising model

NASA Astrophysics Data System (ADS)

Elçi, Eren Metin; Grimm, Jens; Ding, Lijie; Nasrawi, Abrahim; Garoni, Timothy M.; Deng, Youjin

2018-04-01

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.

Towards de novo identification of metabolites by analyzing tandem mass spectra.

PubMed

Böcker, Sebastian; Rasche, Florian

2008-08-15

Mass spectrometry is among the most widely used technologies in proteomics and metabolomics. Being a high-throughput method, it produces large amounts of data that necessitates an automated analysis of the spectra. Clearly, database search methods for protein analysis can easily be adopted to analyze metabolite mass spectra. But for metabolites, de novo interpretation of spectra is even more important than for protein data, because metabolite spectra databases cover only a small fraction of naturally occurring metabolites: even the model plant Arabidopsis thaliana has a large number of enzymes whose substrates and products remain unknown. The field of bio-prospection searches biologically diverse areas for metabolites which might serve as pharmaceuticals. De novo identification of metabolite mass spectra requires new concepts and methods since, unlike proteins, metabolites possess a non-linear molecular structure. In this work, we introduce a method for fully automated de novo identification of metabolites from tandem mass spectra. Mass spectrometry data is usually assumed to be insufficient for identification of molecular structures, so we want to estimate the molecular formula of the unknown metabolite, a crucial step for its identification. The method first calculates all molecular formulas that explain the parent peak mass. Then, a graph is build where vertices correspond to molecular formulas of all peaks in the fragmentation mass spectra, whereas edges correspond to hypothetical fragmentation steps. Our algorithm afterwards calculates the maximum scoring subtree of this graph: each peak in the spectra must be scored at most once, so the subtree shall contain only one explanation per peak. Unfortunately, finding this subtree is NP-hard. We suggest three exact algorithms (including one fixed parameter tractable algorithm) as well as two heuristics to solve the problem. Tests on real mass spectra show that the FPT algorithm and the heuristics solve the problem suitably fast and provide excellent results: for all 32 test compounds the correct solution was among the top five suggestions, for 26 compounds the first suggestion of the exact algorithm was correct. http://www.bio.inf.uni-jena.de/tandemms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wylie, Brian Neil; Moreland, Kenneth D.

Graphs are a vital way of organizing data with complex correlations. A good visualization of a graph can fundamentally change human understanding of the data. Consequently, there is a rich body of work on graph visualization. Although there are many techniques that are effective on small to medium sized graphs (tens of thousands of nodes), there is a void in the research for visualizing massive graphs containing millions of nodes. Sandia is one of the few entities in the world that has the means and motivation to handle data on such a massive scale. For example, homeland security generates graphsmore » from prolific media sources such as television, telephone, and the Internet. The purpose of this project is to provide the groundwork for visualizing such massive graphs. The research provides for two major feature gaps: a parallel, interactive visualization framework and scalable algorithms to make the framework usable to a practical application. Both the frameworks and algorithms are designed to run on distributed parallel computers, which are already available at Sandia. Some features are integrated into the ThreatView{trademark} application and future work will integrate further parallel algorithms.« less

The combination of direct and paired link graphs can boost repetitive genome assembly

PubMed Central

Shi, Wenyu; Ji, Peifeng

2017-01-01

Abstract Currently, most paired link based scaffolding algorithms intrinsically mask the sequences between two linked contigs and bypass their direct link information embedded in the original de Bruijn assembly graph. Such disadvantage substantially complicates the scaffolding process and leads to the inability of resolving repetitive contig assembly. Here we present a novel algorithm, inGAP-sf, for effectively generating high-quality and continuous scaffolds. inGAP-sf achieves this by using a new strategy based on the combination of direct link and paired link graphs, in which direct link is used to increase graph connectivity and to decrease graph complexity and paired link is employed to supervise the traversing process on the direct link graph. Such advantage greatly facilitates the assembly of short-repeat enriched regions. Moreover, a new comprehensive decision model is developed to eliminate the noise routes accompanying with the introduced direct link. Through extensive evaluations on both simulated and real datasets, we demonstrated that inGAP-sf outperforms most of the genome scaffolding algorithms by generating more accurate and continuous assembly, especially for short repetitive regions. PMID:27924003

Optimization of the graph model of the water conduit network, based on the approach of search space reducing

NASA Astrophysics Data System (ADS)

Korovin, Iakov S.; Tkachenko, Maxim G.

2018-03-01

In this paper we present a heuristic approach, improving the efficiency of methods, used for creation of efficient architecture of water distribution networks. The essence of the approach is a procedure of search space reduction the by limiting the range of available pipe diameters that can be used for each edge of the network graph. In order to proceed the reduction, two opposite boundary scenarios for the distribution of flows are analysed, after which the resulting range is further narrowed by applying a flow rate limitation for each edge of the network. The first boundary scenario provides the most uniform distribution of the flow in the network, the opposite scenario created the net with the highest possible flow level. The parameters of both distributions are calculated by optimizing systems of quadratic functions in a confined space, which can be effectively performed with small time costs. This approach was used to modify the genetic algorithm (GA). The proposed GA provides a variable number of variants of each gene, according to the number of diameters in list, taking into account flow restrictions. The proposed approach was implemented to the evaluation of a well-known test network - the Hanoi water distribution network [1], the results of research were compared with a classical GA with an unlimited search space. On the test data, the proposed trip significantly reduced the search space and provided faster and more obvious convergence in comparison with the classical version of GA.

Typical performance of approximation algorithms for NP-hard problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-11-01

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

Information-optimal genome assembly via sparse read-overlap graphs.

PubMed

Shomorony, Ilan; Kim, Samuel H; Courtade, Thomas A; Tse, David N C

2016-09-01

In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. Available at github.com/samhykim/nsg courtade@eecs.berkeley.edu or dntse@stanford.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Convergence of the Graph Allen-Cahn Scheme

NASA Astrophysics Data System (ADS)

Luo, Xiyang; Bertozzi, Andrea L.

2017-05-01

The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.

Integrated Network Decompositions and Dynamic Programming for Graph Optimization (INDDGO)

DOE Office of Scientific and Technical Information (OSTI.GOV)

The INDDGO software package offers a set of tools for finding exact solutions to graph optimization problems via tree decompositions and dynamic programming algorithms. Currently the framework offers serial and parallel (distributed memory) algorithms for finding tree decompositions and solving the maximum weighted independent set problem. The parallel dynamic programming algorithm is implemented on top of the MADNESS task-based runtime.

DOGMA: A Disk-Oriented Graph Matching Algorithm for RDF Databases

NASA Astrophysics Data System (ADS)

Bröcheler, Matthias; Pugliese, Andrea; Subrahmanian, V. S.

RDF is an increasingly important paradigm for the representation of information on the Web. As RDF databases increase in size to approach tens of millions of triples, and as sophisticated graph matching queries expressible in languages like SPARQL become increasingly important, scalability becomes an issue. To date, there is no graph-based indexing method for RDF data where the index was designed in a way that makes it disk-resident. There is therefore a growing need for indexes that can operate efficiently when the index itself resides on disk. In this paper, we first propose the DOGMA index for fast subgraph matching on disk and then develop a basic algorithm to answer queries over this index. This algorithm is then significantly sped up via an optimized algorithm that uses efficient (but correct) pruning strategies when combined with two different extensions of the index. We have implemented a preliminary system and tested it against four existing RDF database systems developed by others. Our experiments show that our algorithm performs very well compared to these systems, with orders of magnitude improvements for complex graph queries.

Man-Made Object Extraction from Remote Sensing Imagery by Graph-Based Manifold Ranking

NASA Astrophysics Data System (ADS)

He, Y.; Wang, X.; Hu, X. Y.; Liu, S. H.

2018-04-01

The automatic extraction of man-made objects from remote sensing imagery is useful in many applications. This paper proposes an algorithm for extracting man-made objects automatically by integrating a graph model with the manifold ranking algorithm. Initially, we estimate a priori value of the man-made objects with the use of symmetric and contrast features. The graph model is established to represent the spatial relationships among pre-segmented superpixels, which are used as the graph nodes. Multiple characteristics, namely colour, texture and main direction, are used to compute the weights of the adjacent nodes. Manifold ranking effectively explores the relationships among all the nodes in the feature space as well as initial query assignment; thus, it is applied to generate a ranking map, which indicates the scores of the man-made objects. The man-made objects are then segmented on the basis of the ranking map. Two typical segmentation algorithms are compared with the proposed algorithm. Experimental results show that the proposed algorithm can extract man-made objects with high recognition rate and low omission rate.

Planning Assembly Of Large Truss Structures In Outer Space

NASA Technical Reports Server (NTRS)

De Mello, Luiz S. Homem; Desai, Rajiv S.

1992-01-01

Report dicusses developmental algorithm used in systematic planning of sequences of operations in which large truss structures assembled in outer space. Assembly sequence represented by directed graph called "assembly graph", in which each arc represents joining of two parts or subassemblies. Algorithm generates assembly graph, working backward from state of complete assembly to initial state, in which all parts disassembled. Working backward more efficient than working forward because it avoids intermediate dead ends.

Patterns and Practices for Future Architectures

DTIC Science & Technology

2014-08-01

14. SUBJECT TERMS computing architecture, graph algorithms, high-performance computing, big data , GPU 15. NUMBER OF PAGES 44 16. PRICE CODE 17...at Vertex 1 6 Figure 4: Data Structures Created by Kernel 1 of Single CPU, List Implementation Using the Graph in the Example from Section 1.2 9...Figure 5: Kernel 2 of Graph500 BFS Reference Implementation: Single CPU, List 10 Figure 6: Data Structures for Sequential CSR Algorithm 12 Figure 7

Multi-scale graph-cut algorithm for efficient water-fat separation.

PubMed

Berglund, Johan; Skorpil, Mikael

2017-09-01

To improve the accuracy and robustness to noise in water-fat separation by unifying the multiscale and graph cut based approaches to B 0 -correction. A previously proposed water-fat separation algorithm that corrects for B 0 field inhomogeneity in 3D by a single quadratic pseudo-Boolean optimization (QPBO) graph cut was incorporated into a multi-scale framework, where field map solutions are propagated from coarse to fine scales for voxels that are not resolved by the graph cut. The accuracy of the single-scale and multi-scale QPBO algorithms was evaluated against benchmark reference datasets. The robustness to noise was evaluated by adding noise to the input data prior to water-fat separation. Both algorithms achieved the highest accuracy when compared with seven previously published methods, while computation times were acceptable for implementation in clinical routine. The multi-scale algorithm was more robust to noise than the single-scale algorithm, while causing only a small increase (+10%) of the reconstruction time. The proposed 3D multi-scale QPBO algorithm offers accurate water-fat separation, robustness to noise, and fast reconstruction. The software implementation is freely available to the research community. Magn Reson Med 78:941-949, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Parallel Algorithms for Switching Edges in Heterogeneous Graphs.

PubMed

Bhuiyan, Hasanuzzaman; Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

2017-06-01

An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors.

Modeling flow and transport in fracture networks using graphs

NASA Astrophysics Data System (ADS)

Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.

Modeling flow and transport in fracture networks using graphs.

PubMed

Karra, S; O'Malley, D; Hyman, J D; Viswanathan, H S; Srinivasan, G

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O(10^{4}) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.

Modeling flow and transport in fracture networks using graphs

DOE PAGES

Karra, S.; O'Malley, D.; Hyman, J. D.; ...

2018-03-09

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizationsmore » of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. In conclusion, the good accuracy and the low computational cost, with O(10 4) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.« less

Modeling flow and transport in fracture networks using graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karra, S.; O'Malley, D.; Hyman, J. D.

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizationsmore » of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. In conclusion, the good accuracy and the low computational cost, with O(10 4) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.« less

Beyond Hosting Capacity: Using Shortest Path Methods to Minimize Upgrade Cost Pathways: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gensollen, Nicolas; Horowitz, Kelsey A; Palmintier, Bryan S

We present in this paper a graph based forwardlooking algorithm applied to distribution planning in the context of distributed PV penetration. We study the target hosting capacity (THC) problem where the objective is to find the cheapest sequence of system upgrades to reach a predefined hosting capacity target value. We show in this paper that commonly used short-term cost minimization approaches lead most of the time to suboptimal solutions. By comparing our method against such myopic techniques on real distribution systems, we show that our algorithm is able to reduce the overall integration costs by looking at future decisions. Becausemore » hosting capacity is hard to compute, this problem requires efficient methods to search the space. We demonstrate here that heuristics using domain specific knowledge can be efficiently used to improve the algorithm performance such that real distribution systems can be studied.« less

Renal cortex segmentation using optimal surface search with novel graph construction.

PubMed

Li, Xiuli; Chen, Xinjian; Yao, Jianhua; Zhang, Xing; Tian, Jie

2011-01-01

In this paper, we propose a novel approach to solve the renal cortex segmentation problem, which has rarely been studied. In this study, the renal cortex segmentation problem is handled as a multiple-surfaces extraction problem, which is solved using the optimal surface search method. We propose a novel graph construction scheme in the optimal surface search to better accommodate multiple surfaces. Different surface sub-graphs are constructed according to their properties, and inter-surface relationships are also modeled in the graph. The proposed method was tested on 17 clinical CT datasets. The true positive volume fraction (TPVF) and false positive volume fraction (FPVF) are 74.10% and 0.08%, respectively. The experimental results demonstrate the effectiveness of the proposed method.

A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem

NASA Astrophysics Data System (ADS)

Jäger, Gerold; Zhang, Weixiong

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.

Graph run-length matrices for histopathological image segmentation.

PubMed

Tosun, Akif Burak; Gunduz-Demir, Cigdem

2011-03-01

The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentation.

Minimum nonuniform graph partitioning with unrelated weights

NASA Astrophysics Data System (ADS)

Makarychev, K. S.; Makarychev, Yu S.

2017-12-01

We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G=(V,E) and k numbers ρ_1,\\dots, ρ_k. The goal is to partition V into k disjoint sets (bins) P_1,\\dots, P_k satisfying \\vert P_i\\vert≤ ρi \\vert V\\vert for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(\\sqrt{log \\vert V\\vert log k}) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints \\vert P_i\\vert ≤ (5+ \\varepsilon)ρi \\vert V\\vert. This algorithm is an improvement upon the O(log \\vert V\\vert)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and Programming (ICALP 2014). Bibliography: 7 titles.

On Parallel Push-Relabel based Algorithms for Bipartite Maximum Matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langguth, Johannes; Azad, Md Ariful; Halappanavar, Mahantesh

2014-07-01

We study multithreaded push-relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial (graph) problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing maximum transversal of a matrix. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a testset comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for themore » parallel push-relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push-relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.« less

Edge Pushing is Equivalent to Vertex Elimination for Computing Hessians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Mu; Pothen, Alex; Hovland, Paul

We prove the equivalence of two different Hessian evaluation algorithms in AD. The first is the Edge Pushing algorithm of Gower and Mello, which may be viewed as a second order Reverse mode algorithm for computing the Hessian. In earlier work, we have derived the Edge Pushing algorithm by exploiting a Reverse mode invariant based on the concept of live variables in compiler theory. The second algorithm is based on eliminating vertices in a computational graph of the gradient, in which intermediate variables are successively eliminated from the graph, and the weights of the edges are updated suitably. We provemore » that if the vertices are eliminated in a reverse topological order while preserving symmetry in the computational graph of the gradient, then the Vertex Elimination algorithm and the Edge Pushing algorithm perform identical computations. In this sense, the two algorithms are equivalent. This insight that unifies two seemingly disparate approaches to Hessian computations could lead to improved algorithms and implementations for computing Hessians. Read More: http://epubs.siam.org/doi/10.1137/1.9781611974690.ch11« less

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

A distributed-memory approximation algorithm for maximum weight perfect bipartite matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azad, Ariful; Buluc, Aydin; Li, Xiaoye S.

We design and implement an efficient parallel approximation algorithm for the problem of maximum weight perfect matching in bipartite graphs, i.e. the problem of finding a set of non-adjacent edges that covers all vertices and has maximum weight. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated by finding good pivots in scalable sparse direct solvers before factorization where sequential implementations of maximum weight perfect matching algorithms, such as those available in MC64, are widely used due to the lack of scalable alternatives. To overcome this limitation, we proposemore » a fully parallel distributed memory algorithm that first generates a perfect matching and then searches for weightaugmenting cycles of length four in parallel and iteratively augments the matching with a vertex disjoint set of such cycles. For most practical problems the weights of the perfect matchings generated by our algorithm are very close to the optimum. An efficient implementation of the algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer and can solve instances that are too large to be handled by a single node using the sequential algorithm.« less

A multicolour graph as a complete topological invariant for \\Omega-stable flows without periodic trajectories on surfaces

NASA Astrophysics Data System (ADS)

Kruglov, V. E.; Malyshev, D. S.; Pochinka, O. V.

2018-01-01

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph. Bibliography: 17 titles.

Graph Drawing Aesthetics-Created by Users, Not Algorithms.

PubMed

Purchase, H C; Pilcher, C; Plimmer, B

2012-01-01

Prior empirical work on layout aesthetics for graph drawing algorithms has concentrated on the interpretation of existing graph drawings. We report on experiments which focus on the creation and layout of graph drawings: participants were asked to draw graphs based on adjacency lists, and to lay them out "nicely." Two interaction methods were used for creating the drawings: a sketch interface which allows for easy, natural hand movements, and a formal point-and-click interface similar to a typical graph editing system. We find, in common with many other studies, that removing edge crossings is the most significant aesthetic, but also discover that aligning nodes and edges to an underlying grid is important. We observe that the aesthetics favored by participants during creation of a graph drawing are often not evident in the final product and that the participants did not make a clear distinction between the processes of creation and layout. Our results suggest that graph drawing systems should integrate automatic layout with the user's manual editing process, and provide facilities to support grid-based graph creation.

Finding minimum-quotient cuts in planar graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, J.K.; Phillips, C.A.

Given a graph G = (V, E) where each vertex v {element_of} V is assigned a weight w(v) and each edge e {element_of} E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and {bar S} is c(S, {bar S})/min{l_brace}w(S), w(S){r_brace}, where c(S, {bar S}) is the sum of the costs of the edges crossing the cut and w(S) and w({bar S}) are the sum of the weights of the vertices in S and {bar S}, respectively. The problem of finding a cut whose quotient is minimum for a graph hasmore » in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,{bar S}) minimizing c(S,{bar S}) subject to the constraint bW {le} w(S) {le} (1 {minus} b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b {le} {1/2}. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao`s algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao`s most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less

Finding minimum-quotient cuts in planar graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, J.K.; Phillips, C.A.

Given a graph G = (V, E) where each vertex v [element of] V is assigned a weight w(v) and each edge e [element of] E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and [bar S] is c(S, [bar S])/min[l brace]w(S), w(S)[r brace], where c(S, [bar S]) is the sum of the costs of the edges crossing the cut and w(S) and w([bar S]) are the sum of the weights of the vertices in S and [bar S], respectively. The problem of finding a cut whose quotient is minimummore » for a graph has in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,[bar S]) minimizing c(S,[bar S]) subject to the constraint bW [le] w(S) [le] (1 [minus] b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b [le] [1/2]. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao's algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao's most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less

Toward the optimization of normalized graph Laplacian.

PubMed

Xie, Bo; Wang, Meng; Tao, Dacheng

2011-04-01

Normalized graph Laplacian has been widely used in many practical machine learning algorithms, e.g., spectral clustering and semisupervised learning. However, all of them use the Euclidean distance to construct the graph Laplacian, which does not necessarily reflect the inherent distribution of the data. In this brief, we propose a method to directly optimize the normalized graph Laplacian by using pairwise constraints. The learned graph is consistent with equivalence and nonequivalence pairwise relationships, and thus it can better represent similarity between samples. Meanwhile, our approach, unlike metric learning, automatically determines the scale factor during the optimization. The learned normalized Laplacian matrix can be directly applied in spectral clustering and semisupervised learning algorithms. Comprehensive experiments demonstrate the effectiveness of the proposed approach.

Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy

NASA Astrophysics Data System (ADS)

Magen, Avner; Moharrami, Mohammad

This work provides a Linear Programming-based Polynomial Time Approximation Scheme (PTAS) for two classical NP-hard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of when approximation is required) of rounds of the so-called Sherali-Adams Lift-and-Project system. needed to obtain a -approximation, where f is some function that depends only on the graph that should be avoided as a minor. The problem we discuss are the well-studied problems, the and problems. An curious fact we expose is that in the world of minor-free graph, the is harder in some sense than the.

Global Binary Optimization on Graphs for Classification of High Dimensional Data

DTIC Science & Technology

2014-09-01

Buades et al . in [10] introduce a new non-local means algorithm for image denoising and compare it to some of the best methods. In [28], Grady de...scribes a random walk algorithm for image seg- mentation using the solution to a Dirichlet prob- lem. Elmoataz et al . present generalizations of the...graph Laplacian [19] for image denoising and man- ifold smoothing. Couprie et al . in [16] propose a parameterized graph-based energy function that unifies

A software tool for dataflow graph scheduling

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1994-01-01

A graph-theoretic design process and software tool is presented for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described using a dataflow graph and are intended to be executed repetitively on multiple processors. The dataflow paradigm is very useful in exposing the parallelism inherent in algorithms. It provides a graphical and mathematical model which describes a partial ordering of algorithm tasks based on data precedence.

Method for concurrent execution of primitive operations by dynamically assigning operations based upon computational marked graph and availability of data

NASA Technical Reports Server (NTRS)

Mielke, Roland V. (Inventor); Stoughton, John W. (Inventor)

1990-01-01

Computationally complex primitive operations of an algorithm are executed concurrently in a plurality of functional units under the control of an assignment manager. The algorithm is preferably defined as a computationally marked graph contianing data status edges (paths) corresponding to each of the data flow edges. The assignment manager assigns primitive operations to the functional units and monitors completion of the primitive operations to determine data availability using the computational marked graph of the algorithm. All data accessing of the primitive operations is performed by the functional units independently of the assignment manager.

Dynamic airspace configuration algorithms for next generation air transportation system

NASA Astrophysics Data System (ADS)

Wei, Jian

The National Airspace System (NAS) is under great pressure to safely and efficiently handle the record-high air traffic volume nowadays, and will face even greater challenge to keep pace with the steady increase of future air travel demand, since the air travel demand is projected to increase to two to three times the current level by 2025. The inefficiency of traffic flow management initiatives causes severe airspace congestion and frequent flight delays, which cost billions of economic losses every year. To address the increasingly severe airspace congestion and delays, the Next Generation Air Transportation System (NextGen) is proposed to transform the current static and rigid radar based system to a dynamic and flexible satellite based system. New operational concepts such as Dynamic Airspace Configuration (DAC) have been under development to allow more flexibility required to mitigate the demand-capacity imbalances in order to increase the throughput of the entire NAS. In this dissertation, we address the DAC problem in the en route and terminal airspace under the framework of NextGen. We develop a series of algorithms to facilitate the implementation of innovative concepts relevant with DAC in both the en route and terminal airspace. We also develop a performance evaluation framework for comprehensive benefit analyses on different aspects of future sector design algorithms. First, we complete a graph based sectorization algorithm for DAC in the en route airspace, which models the underlying air route network with a weighted graph, converts the sectorization problem into the graph partition problem, partitions the weighted graph with an iterative spectral bipartition method, and constructs the sectors from the partitioned graph. The algorithm uses a graph model to accurately capture the complex traffic patterns of the real flights, and generates sectors with high efficiency while evenly distributing the workload among the generated sectors. We further improve the robustness and efficiency of the graph based DAC algorithm by incorporating the Multilevel Graph Partitioning (MGP) method into the graph model, and develop a MGP based sectorization algorithm for DAC in the en route airspace. In a comprehensive benefit analysis, the performance of the proposed algorithms are tested in numerical simulations with Enhanced Traffic Management System (ETMS) data. Simulation results demonstrate that the algorithmically generated sectorizations outperform the current sectorizations in different sectors for different time periods. Secondly, based on our experience with DAC in the en route airspace, we further study the sectorization problem for DAC in the terminal airspace. The differences between the en route and terminal airspace are identified, and their influence on the terminal sectorization is analyzed. After adjusting the graph model to better capture the unique characteristics of the terminal airspace and the requirements of terminal sectorization, we develop a graph based geometric sectorization algorithm for DAC in the terminal airspace. Moreover, the graph based model is combined with the region based sector design method to better handle the complicated geometric and operational constraints in the terminal sectorization problem. In the benefit analysis, we identify the contributing factors to terminal controller workload, define evaluation metrics, and develop a bebefit analysis framework for terminal sectorization evaluation. With the evaluation framework developed, we demonstrate the improvements on the current sectorizations with real traffic data collected from several major international airports in the U.S., and conduct a detailed analysis on the potential benefits of dynamic reconfiguration in the terminal airspace. Finally, in addition to the research on the macroscopic behavior of a large number of aircraft, we also study the dynamical behavior of individual aircraft from the perspective of traffic flow management. We formulate the mode-confusion problem as hybrid estimation problem, and develop a state estimation algorithm for the linear hybrid system with continuous-state-dependent transitions based on sparse observations. We also develop an estimated time of arrival prediction algorithm based on the state-dependent transition hybrid estimation algorithm, whose performance is demonstrated with simulations on the landing procedure following the Continuous Descend Approach (CDA) profile.

New Graph Models and Algorithms for Detecting Salient Structures from Cluttered Images

DTIC Science & Technology

2010-02-24

Development of graph models and algorithms to detect boundaries that show certain levels of symmetry, an important geometric property of many...Bookstein. Morphometric tools for landmark data. Cambridge University Press, 1991. [8] F. L. Bookstein. Principal warps: Thin-plate splines and the

An efficient randomized algorithm for contact-based NMR backbone resonance assignment.

PubMed

Kamisetty, Hetunandan; Bailey-Kellogg, Chris; Pandurangan, Gopal

2006-01-15

Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call 'contact-based', seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (nuclear Overhauser enhancement spectroscopy, NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were 'close enough'. Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g. for alpha-helices and beta-sheets) within a graph and by mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise. This paper develops, analyzes and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500% noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet datasets. Our approach is able to eliminate a large majority of noise edges and to uncover large consistent sets of interactions. Our algorithm has been implemented in the platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

Anomaly detection in hyperspectral imagery: statistics vs. graph-based algorithms

NASA Astrophysics Data System (ADS)

Berkson, Emily E.; Messinger, David W.

2016-05-01

Anomaly detection (AD) algorithms are frequently applied to hyperspectral imagery, but different algorithms produce different outlier results depending on the image scene content and the assumed background model. This work provides the first comparison of anomaly score distributions between common statistics-based anomaly detection algorithms (RX and subspace-RX) and the graph-based Topological Anomaly Detector (TAD). Anomaly scores in statistical AD algorithms should theoretically approximate a chi-squared distribution; however, this is rarely the case with real hyperspectral imagery. The expected distribution of scores found with graph-based methods remains unclear. We also look for general trends in algorithm performance with varied scene content. Three separate scenes were extracted from the hyperspectral MegaScene image taken over downtown Rochester, NY with the VIS-NIR-SWIR ProSpecTIR instrument. In order of most to least cluttered, we study an urban, suburban, and rural scene. The three AD algorithms were applied to each scene, and the distributions of the most anomalous 5% of pixels were compared. We find that subspace-RX performs better than RX, because the data becomes more normal when the highest variance principal components are removed. We also see that compared to statistical detectors, anomalies detected by TAD are easier to separate from the background. Due to their different underlying assumptions, the statistical and graph-based algorithms highlighted different anomalies within the urban scene. These results will lead to a deeper understanding of these algorithms and their applicability across different types of imagery.

Multiple graph regularized protein domain ranking.

PubMed

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-11-19

Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

Multiple graph regularized protein domain ranking

PubMed Central

2012-01-01

Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. PMID:23157331

Coverability graphs for a class of synchronously executed unbounded Petri net

NASA Technical Reports Server (NTRS)

Stotts, P. David; Pratt, Terrence W.

1990-01-01

After detailing a variant of the concurrent-execution rule for firing of maximal subsets, in which the simultaneous firing of conflicting transitions is prohibited, an algorithm is constructed for generating the coverability graph of a net executed under this synchronous firing rule. The omega insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates. It is accordingly shown that the set of nets on which the algorithm terminates includes the 'conflict-free' class.

Faster quantum walk search on a weighted graph

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2015-09-01

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ (N3 /4) . We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ (√{N }) . To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

Graph Design via Convex Optimization: Online and Distributed Perspectives

NASA Astrophysics Data System (ADS)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation problems in sensor networks, multi-agent coordination. Distributed optimization aims to optimize a global objective function formed by summation of coupled local functions over a graph via only local communication and computation. We developed a weighted proximal ADMM for distributed optimization using graph structure. This fully distributed, single-loop algorithm allows simultaneous updates and can be viewed as a generalization of existing algorithms. More importantly, we achieve faster convergence by jointly designing graph weights and algorithm parameters. Finally, we propose a new problem on networks called Online Network Formation Problem: starting with a base graph and a set of candidate edges, at each round of the game, player one first chooses a candidate edge and reveals it to player two, then player two decides whether to accept it; player two can only accept limited number of edges and make online decisions with the goal to achieve the best properties of the synthesized network. The network properties considered include the number of spanning trees, algebraic connectivity and total effective resistance. These network formation games arise in a variety of cooperative multiagent systems. We propose a primal-dual algorithm framework for the general online network formation game, and analyze the algorithm performance by the competitive ratio and regret.

Quantum speedup in solving the maximal-clique problem

NASA Astrophysics Data System (ADS)

Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang

2018-03-01

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

Fitchi: haplotype genealogy graphs based on the Fitch algorithm.

PubMed

Matschiner, Michael

2016-04-15

: In population genetics and phylogeography, haplotype genealogy graphs are important tools for the visualization of population structure based on sequence data. In this type of graph, node sizes are often drawn in proportion to haplotype frequencies and edge lengths represent the minimum number of mutations separating adjacent nodes. I here present Fitchi, a new program that produces publication-ready haplotype genealogy graphs based on the Fitch algorithm. http://www.evoinformatics.eu/fitchi.htm : michaelmatschiner@mac.com Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

PubMed

Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

2017-01-01

An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

Overview and extensions of a system for routing directed graphs on SIMD architectures

NASA Technical Reports Server (NTRS)

Tomboulian, Sherryl

1988-01-01

Many problems can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from adjacent vertices. A method is given for parallelizing such problems on an SIMD machine model that uses only nearest neighbor connections for communication, and has no facility for local indirect addressing. Each vertex of the graph will be assigned to a processor in the machine. Rules for a labeling are introduced that support the use of a simple algorithm for movement of data along the edges of the graph. Additional algorithms are defined for addition and deletion of edges. Modifying or adding a new edge takes the same time as parallel traversal. This combination of architecture and algorithms defines a system that is relatively simple to build and can do fast graph processing. All edges can be traversed in parallel in time O(T), where T is empirically proportional to the average path length in the embedding times the average degree of the graph. Additionally, researchers present an extension to the above method which allows for enhanced performance by allowing some broadcasting capabilities.

A New Augmentation Based Algorithm for Extracting Maximal Chordal Subgraphs.

PubMed

Bhowmick, Sanjukta; Chen, Tzu-Yi; Halappanavar, Mahantesh

2015-02-01

A graph is chordal if every cycle of length greater than three contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms' parallelizability. In this paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. We experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.

A system for routing arbitrary directed graphs on SIMD architectures

NASA Technical Reports Server (NTRS)

Tomboulian, Sherryl

1987-01-01

There are many problems which can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from connecting vertices. A method is given for parallelizing such problems on an SIMD machine model that is bit-serial and uses only nearest neighbor connections for communication. Each vertex of the graph will be assigned to a processor in the machine. Algorithms are given that will be used to implement movement of data along the arcs of the graph. This architecture and algorithms define a system that is relatively simple to build and can do graph processing. All arcs can be transversed in parallel in time O(T), where T is empirically proportional to the diameter of the interconnection network times the average degree of the graph. Modifying or adding a new arc takes the same time as parallel traversal.

TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

PubMed

Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

2016-01-01

We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

Efficient and Scalable Graph Similarity Joins in MapReduce

PubMed Central

Chen, Yifan; Zhang, Weiming; Tang, Jiuyang

2014-01-01

Along with the emergence of massive graph-modeled data, it is of great importance to investigate graph similarity joins due to their wide applications for multiple purposes, including data cleaning, and near duplicate detection. This paper considers graph similarity joins with edit distance constraints, which return pairs of graphs such that their edit distances are no larger than a given threshold. Leveraging the MapReduce programming model, we propose MGSJoin, a scalable algorithm following the filtering-verification framework for efficient graph similarity joins. It relies on counting overlapping graph signatures for filtering out nonpromising candidates. With the potential issue of too many key-value pairs in the filtering phase, spectral Bloom filters are introduced to reduce the number of key-value pairs. Furthermore, we integrate the multiway join strategy to boost the verification, where a MapReduce-based method is proposed for GED calculation. The superior efficiency and scalability of the proposed algorithms are demonstrated by extensive experimental results. PMID:25121135

Efficient and scalable graph similarity joins in MapReduce.

PubMed

Chen, Yifan; Zhao, Xiang; Xiao, Chuan; Zhang, Weiming; Tang, Jiuyang

2014-01-01

Along with the emergence of massive graph-modeled data, it is of great importance to investigate graph similarity joins due to their wide applications for multiple purposes, including data cleaning, and near duplicate detection. This paper considers graph similarity joins with edit distance constraints, which return pairs of graphs such that their edit distances are no larger than a given threshold. Leveraging the MapReduce programming model, we propose MGSJoin, a scalable algorithm following the filtering-verification framework for efficient graph similarity joins. It relies on counting overlapping graph signatures for filtering out nonpromising candidates. With the potential issue of too many key-value pairs in the filtering phase, spectral Bloom filters are introduced to reduce the number of key-value pairs. Furthermore, we integrate the multiway join strategy to boost the verification, where a MapReduce-based method is proposed for GED calculation. The superior efficiency and scalability of the proposed algorithms are demonstrated by extensive experimental results.

Path planning for assembly of strut-based structures. Thesis

NASA Technical Reports Server (NTRS)

Muenger, Rolf

1991-01-01

A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

2017-01-01

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

Development of antibiotic regimens using graph based evolutionary algorithms.

PubMed

Corns, Steven M; Ashlock, Daniel A; Bryden, Kenneth M

2013-12-01

This paper examines the use of evolutionary algorithms in the development of antibiotic regimens given to production animals. A model is constructed that combines the lifespan of the animal and the bacteria living in the animal's gastro-intestinal tract from the early finishing stage until the animal reaches market weight. This model is used as the fitness evaluation for a set of graph based evolutionary algorithms to assess the impact of diversity control on the evolving antibiotic regimens. The graph based evolutionary algorithms have two objectives: to find an antibiotic treatment regimen that maintains the weight gain and health benefits of antibiotic use and to reduce the risk of spreading antibiotic resistant bacteria. This study examines different regimens of tylosin phosphate use on bacteria populations divided into Gram positive and Gram negative types, with a focus on Campylobacter spp. Treatment regimens were found that provided decreased antibiotic resistance relative to conventional methods while providing nearly the same benefits as conventional antibiotic regimes. By using a graph to control the information flow in the evolutionary algorithm, a variety of solutions along the Pareto front can be found automatically for this and other multi-objective problems. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

OpenMP Parallelization and Optimization of Graph-Based Machine Learning Algorithms

DOE PAGES

Meng, Zhaoyi; Koniges, Alice; He, Yun Helen; ...

2016-09-21

In this paper, we investigate the OpenMP parallelization and optimization of two novel data classification algorithms. The new algorithms are based on graph and PDE solution techniques and provide significant accuracy and performance advantages over traditional data classification algorithms in serial mode. The methods leverage the Nystrom extension to calculate eigenvalue/eigenvectors of the graph Laplacian and this is a self-contained module that can be used in conjunction with other graph-Laplacian based methods such as spectral clustering. We use performance tools to collect the hotspots and memory access of the serial codes and use OpenMP as the parallelization language to parallelizemore » the most time-consuming parts. Where possible, we also use library routines. We then optimize the OpenMP implementations and detail the performance on traditional supercomputer nodes (in our case a Cray XC30), and test the optimization steps on emerging testbed systems based on Intel’s Knights Corner and Landing processors. We show both performance improvement and strong scaling behavior. Finally, a large number of optimization techniques and analyses are necessary before the algorithm reaches almost ideal scaling.« less

A Multilevel Gamma-Clustering Layout Algorithm for Visualization of Biological Networks

PubMed Central

Hruz, Tomas; Lucas, Christoph; Laule, Oliver; Zimmermann, Philip

2013-01-01

Visualization of large complex networks has become an indispensable part of systems biology, where organisms need to be considered as one complex system. The visualization of the corresponding network is challenging due to the size and density of edges. In many cases, the use of standard visualization algorithms can lead to high running times and poorly readable visualizations due to many edge crossings. We suggest an approach that analyzes the structure of the graph first and then generates a new graph which contains specific semantic symbols for regular substructures like dense clusters. We propose a multilevel gamma-clustering layout visualization algorithm (MLGA) which proceeds in three subsequent steps: (i) a multilevel γ-clustering is used to identify the structure of the underlying network, (ii) the network is transformed to a tree, and (iii) finally, the resulting tree which shows the network structure is drawn using a variation of a force-directed algorithm. The algorithm has a potential to visualize very large networks because it uses modern clustering heuristics which are optimized for large graphs. Moreover, most of the edges are removed from the visual representation which allows keeping the overview over complex graphs with dense subgraphs. PMID:23864855

On the modification Highly Connected Subgraphs (HCS) algorithm in graph clustering for weighted graph

NASA Astrophysics Data System (ADS)

Albirri, E. R.; Sugeng, K. A.; Aldila, D.

2018-04-01

Nowadays, in the modern world, since technology and human civilization start to progress, all city in the world is almost connected. The various places in this world are easier to visit. It is an impact of transportation technology and highway construction. The cities which have been connected can be represented by graph. Graph clustering is one of ways which is used to answer some problems represented by graph. There are some methods in graph clustering to solve the problem spesifically. One of them is Highly Connected Subgraphs (HCS) method. HCS is used to identify cluster based on the graph connectivity k for graph G. The connectivity in graph G is denoted by k(G)> \\frac{n}{2} that n is the total of vertices in G, then it is called as HCS or the cluster. This research used literature review and completed with simulation of program in a software. We modified HCS algorithm by using weighted graph. The modification is located in the Process Phase. Process Phase is used to cut the connected graph G into two subgraphs H and \\bar{H}. We also made a program by using software Octave-401. Then we applied the data of Flight Routes Mapping of One of Airlines in Indonesia to our program.

EClerize: A customized force-directed graph drawing algorithm for biological graphs with EC attributes.

PubMed

Danaci, Hasan Fehmi; Cetin-Atalay, Rengul; Atalay, Volkan

2018-03-26

Visualizing large-scale data produced by the high throughput experiments as a biological graph leads to better understanding and analysis. This study describes a customized force-directed layout algorithm, EClerize, for biological graphs that represent pathways in which the nodes are associated with Enzyme Commission (EC) attributes. The nodes with the same EC class numbers are treated as members of the same cluster. Positions of nodes are then determined based on both the biological similarity and the connection structure. EClerize minimizes the intra-cluster distance, that is the distance between the nodes of the same EC cluster and maximizes the inter-cluster distance, that is the distance between two distinct EC clusters. EClerize is tested on a number of biological pathways and the improvement brought in is presented with respect to the original algorithm. EClerize is available as a plug-in to cytoscape ( http://apps.cytoscape.org/apps/eclerize ).

Enhancing Community Detection By Affinity-based Edge Weighting Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo, Andy; Sanders, Geoffrey; Henson, Van

Community detection refers to an important graph analytics problem of finding a set of densely-connected subgraphs in a graph and has gained a great deal of interest recently. The performance of current community detection algorithms is limited by an inherent constraint of unweighted graphs that offer very little information on their internal community structures. In this paper, we propose a new scheme to address this issue that weights the edges in a given graph based on recently proposed vertex affinity. The vertex affinity quantifies the proximity between two vertices in terms of their clustering strength, and therefore, it is idealmore » for graph analytics applications such as community detection. We also demonstrate that the affinity-based edge weighting scheme can improve the performance of community detection algorithms significantly.« less

Efficient searching in meshfree methods

NASA Astrophysics Data System (ADS)

Olliff, James; Alford, Brad; Simkins, Daniel C.

2018-04-01

Meshfree methods such as the Reproducing Kernel Particle Method and the Element Free Galerkin method have proven to be excellent choices for problems involving complex geometry, evolving topology, and large deformation, owing to their ability to model the problem domain without the constraints imposed on the Finite Element Method (FEM) meshes. However, meshfree methods have an added computational cost over FEM that come from at least two sources: increased cost of shape function evaluation and the determination of adjacency or connectivity. The focus of this paper is to formally address the types of adjacency information that arises in various uses of meshfree methods; a discussion of available techniques for computing the various adjacency graphs; propose a new search algorithm and data structure; and finally compare the memory and run time performance of the methods.

Distributed Sensing and Processing: A Graphical Model Approach

DTIC Science & Technology

2005-11-30

that Ramanujan graph toplogies maximize the convergence rate of distributed detection consensus algorithms, improving over three orders of...small world type network designs. 14. SUBJECT TERMS Ramanujan graphs, sensor network topology, sensor network...that Ramanujan graphs, for which there are explicit algebraic constructions, have large eigenratios, converging much faster than structured graphs

Solving graph data issues using a layered architecture approach with applications to web spam detection.

PubMed

Scarselli, Franco; Tsoi, Ah Chung; Hagenbuchner, Markus; Noi, Lucia Di

2013-12-01

This paper proposes the combination of two state-of-the-art algorithms for processing graph input data, viz., the probabilistic mapping graph self organizing map, an unsupervised learning approach, and the graph neural network, a supervised learning approach. We organize these two algorithms in a cascade architecture containing a probabilistic mapping graph self organizing map, and a graph neural network. We show that this combined approach helps us to limit the long-term dependency problem that exists when training the graph neural network resulting in an overall improvement in performance. This is demonstrated in an application to a benchmark problem requiring the detection of spam in a relatively large set of web sites. It is found that the proposed method produces results which reach the state of the art when compared with some of the best results obtained by others using quite different approaches. A particular strength of our method is its applicability towards any input domain which can be represented as a graph. Copyright © 2013 Elsevier Ltd. All rights reserved.

X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

DTIC Science & Technology

2017-09-01

INTRODUCTION 1 3 METHODS , ASUMPTIONS, AND PROCEDURES 2 Software Abstractions for Graph Analytic Applications 2 High performance Platforms for Graph Processing...data is stored in a distributed file system. 3 METHODS , ASUMPTIONS, AND PROCEDURES Software Abstractions for Graph Analytic Applications To...implementations of novel methods for networks analysis: several methods for detection of overlapping communities, personalized PageRank, node embeddings into a d

Resource utilization model for the algorithm to architecture mapping model

NASA Technical Reports Server (NTRS)

Stoughton, John W.; Patel, Rakesh R.

1993-01-01

The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories.

An effective trust-based recommendation method using a novel graph clustering algorithm

NASA Astrophysics Data System (ADS)

Moradi, Parham; Ahmadian, Sajad; Akhlaghian, Fardin

2015-10-01

Recommender systems are programs that aim to provide personalized recommendations to users for specific items (e.g. music, books) in online sharing communities or on e-commerce sites. Collaborative filtering methods are important and widely accepted types of recommender systems that generate recommendations based on the ratings of like-minded users. On the other hand, these systems confront several inherent issues such as data sparsity and cold start problems, caused by fewer ratings against the unknowns that need to be predicted. Incorporating trust information into the collaborative filtering systems is an attractive approach to resolve these problems. In this paper, we present a model-based collaborative filtering method by applying a novel graph clustering algorithm and also considering trust statements. In the proposed method first of all, the problem space is represented as a graph and then a sparsest subgraph finding algorithm is applied on the graph to find the initial cluster centers. Then, the proposed graph clustering algorithm is performed to obtain the appropriate users/items clusters. Finally, the identified clusters are used as a set of neighbors to recommend unseen items to the current active user. Experimental results based on three real-world datasets demonstrate that the proposed method outperforms several state-of-the-art recommender system methods.

A note on the stability and discriminability of graph-based features for classification problems in digital pathology

NASA Astrophysics Data System (ADS)

Cruz-Roa, Angel; Xu, Jun; Madabhushi, Anant

2015-01-01

Nuclear architecture or the spatial arrangement of individual cancer nuclei on histopathology images has been shown to be associated with different grades and differential risk for a number of solid tumors such as breast, prostate, and oropharyngeal. Graph-based representations of individual nuclei (nuclei representing the graph nodes) allows for mining of quantitative metrics to describe tumor morphology. These graph features can be broadly categorized into global and local depending on the type of graph construction method. While a number of local graph (e.g. Cell Cluster Graphs) and global graph (e.g. Voronoi, Delaunay Triangulation, Minimum Spanning Tree) features have been shown to associated with cancer grade, risk, and outcome for different cancer types, the sensitivity of the preceding segmentation algorithms in identifying individual nuclei can have a significant bearing on the discriminability of the resultant features. This therefore begs the question as to which features while being discriminative of cancer grade and aggressiveness are also the most resilient to the segmentation errors. These properties are particularly desirable in the context of digital pathology images, where the method of slide preparation, staining, and type of nuclear segmentation algorithm employed can all dramatically affect the quality of the nuclear graphs and corresponding features. In this paper we evaluated the trade off between discriminability and stability of both global and local graph-based features in conjunction with a few different segmentation algorithms and in the context of two different histopathology image datasets of breast cancer from whole-slide images (WSI) and tissue microarrays (TMA). Specifically in this paper we investigate a few different performance measures including stability, discriminability and stability vs discriminability trade off, all of which are based on p-values from the Kruskal-Wallis one-way analysis of variance for local and global graph features. Apart from identifying the set of local and global features that satisfied the trade off between stability and discriminability, our most interesting finding was that a simple segmentation method was sufficient to identify the most discriminant features for invasive tumour detection in TMAs, whereas for tumour grading in WSI, the graph based features were more sensitive to the accuracy of the segmentation algorithm employed.

A new augmentation based algorithm for extracting maximal chordal subgraphs

DOE PAGES

Bhowmick, Sanjukta; Chen, Tzu-Yi; Halappanavar, Mahantesh

2014-10-18

If every cycle of a graph is chordal length greater than three then it contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms’more » parallelizability. In our paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. Finally, we experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.« less

Learning context-sensitive shape similarity by graph transduction.

PubMed

Bai, Xiang; Yang, Xingwei; Latecki, Longin Jan; Liu, Wenyu; Tu, Zhuowen

2010-05-01

Shape similarity and shape retrieval are very important topics in computer vision. The recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes. In this paper, we provide a new perspective to this problem by considering the existing shapes as a group, and study their similarity measures to the query shape in a graph structure. Our method is general and can be built on top of any existing shape similarity measure. For a given similarity measure, a new similarity is learned through graph transduction. The new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query. The basic idea here is related to PageRank ranking, which forms a foundation of Google Web search. The presented experimental results demonstrate that the proposed approach yields significant improvements over the state-of-art shape matching algorithms. We obtained a retrieval rate of 91.61 percent on the MPEG-7 data set, which is the highest ever reported in the literature. Moreover, the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering.

System for line drawings interpretation

NASA Astrophysics Data System (ADS)

Boatto, L.; Consorti, Vincenzo; Del Buono, Monica; Eramo, Vincenzo; Esposito, Alessandra; Melcarne, F.; Meucci, Mario; Mosciatti, M.; Tucci, M.; Morelli, Arturo

1992-08-01

This paper describes an automatic system that extracts information from line drawings, in order to feed CAD or GIS systems. The line drawings that we analyze contain interconnected thin lines, dashed lines, text, and symbols. Characters and symbols may overlap with lines. Our approach is based on the properties of the run representation of a binary image that allow giving the image a graph structure. Using this graph structure, several algorithms have been designed to identify, directly in the raster image, straight segments, dashed lines, text, symbols, hatching lines, etc. Straight segments and dashed lines are converted into vectors, with high accuracy and good noise immunity. Characters and symbols are recognized by means of a recognizer, specifically developed for this application, designed to be insensitive to rotation and scaling. Subsequent processing steps include an `intelligent'' search through the graph in order to detect closed polygons, dashed lines, text strings, and other higher-level logical entities, followed by the identification of relationships (adjacency, inclusion, etc.) between them. Relationships are further translated into a formal description of the drawing. The output of the system can be used as input to a Geographic Information System package. The system is currently used by the Italian Land Register Authority to process cadastral maps.

Compacting de Bruijn graphs from sequencing data quickly and in low memory.

PubMed

Chikhi, Rayan; Limasset, Antoine; Medvedev, Paul

2016-06-15

As the quantity of data per sequencing experiment increases, the challenges of fragment assembly are becoming increasingly computational. The de Bruijn graph is a widely used data structure in fragment assembly algorithms, used to represent the information from a set of reads. Compaction is an important data reduction step in most de Bruijn graph based algorithms where long simple paths are compacted into single vertices. Compaction has recently become the bottleneck in assembly pipelines, and improving its running time and memory usage is an important problem. We present an algorithm and a tool bcalm 2 for the compaction of de Bruijn graphs. bcalm 2 is a parallel algorithm that distributes the input based on a minimizer hashing technique, allowing for good balance of memory usage throughout its execution. For human sequencing data, bcalm 2 reduces the computational burden of compacting the de Bruijn graph to roughly an hour and 3 GB of memory. We also applied bcalm 2 to the 22 Gbp loblolly pine and 20 Gbp white spruce sequencing datasets. Compacted graphs were constructed from raw reads in less than 2 days and 40 GB of memory on a single machine. Hence, bcalm 2 is at least an order of magnitude more efficient than other available methods. Source code of bcalm 2 is freely available at: https://github.com/GATB/bcalm rayan.chikhi@univ-lille1.fr. © The Author 2016. Published by Oxford University Press.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

PubMed

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which verticesmore » (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.« less

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

PubMed Central

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagberg, Aric; Swart, Pieter; S Chult, Daniel

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility mades NetworkX ideal for representing networks found in many different scientific fields. In addition to the basic data structures many graph algorithms are implemented for calculating network properties and structure measures: shortest paths, betweenness centrality, clustering, and degree distributionmore » and many more. NetworkX can read and write various graph formats for eash exchange with existing data, and provides generators for many classic graphs and popular graph models, such as the Erdoes-Renyi, Small World, and Barabasi-Albert models, are included. The ease-of-use and flexibility of the Python programming language together with connection to the SciPy tools make NetworkX a powerful tool for scientific computations. We discuss some of our recent work studying synchronization of coupled oscillators to demonstrate how NetworkX enables research in the field of computational networks.« less

Multi-A Graph Patrolling and Partitioning

NASA Astrophysics Data System (ADS)

Elor, Y.; Bruckstein, A. M.

2012-12-01

We introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph.

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

2013-07-01

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

Efficient Extraction of High Centrality Vertices in Distributed Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumbhare, Alok; Frincu, Marc; Raghavendra, Cauligi S.

2014-09-09

Betweenness centrality (BC) is an important measure for identifying high value or critical vertices in graphs, in variety of domains such as communication networks, road networks, and social graphs. However, calculating betweenness values is prohibitively expensive and, more often, domain experts are interested only in the vertices with the highest centrality values. In this paper, we first propose a partition-centric algorithm (MS-BC) to calculate BC for a large distributed graph that optimizes resource utilization and improves overall performance. Further, we extend the notion of approximate BC by pruning the graph and removing a subset of edges and vertices that contributemore » the least to the betweenness values of other vertices (MSL-BC), which further improves the runtime performance. We evaluate the proposed algorithms using a mix of real-world and synthetic graphs on an HPC cluster and analyze its strengths and weaknesses. The experimental results show an improvement in performance of upto 12x for large sparse graphs as compared to the state-of-the-art, and at the same time highlights the need for better partitioning methods to enable a balanced workload across partitions for unbalanced graphs such as small-world or power-law graphs.« less

Tensor Spectral Clustering for Partitioning Higher-order Network Structures.

PubMed

Benson, Austin R; Gleich, David F; Leskovec, Jure

2015-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

PubMed Central

Benson, Austin R.; Gleich, David F.; Leskovec, Jure

2016-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399

Exploratory Item Classification Via Spectral Graph Clustering

PubMed Central

Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Xu, Gongjun; Ying, Zhiliang

2017-01-01

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster analysis. The method is computationally efficient, effective for data with missing or incomplete responses, easy to implement, and often outperforms traditional clustering algorithms in the context of high dimensionality. The spectral clustering algorithm is based on graph theory, a branch of mathematics that studies the properties of graphs. The algorithm first constructs a graph of items, characterizing the similarity structure among items. It then extracts item clusters based on the graphical structure, grouping similar items together. The proposed method is evaluated through simulations and an application to the revised Eysenck Personality Questionnaire. PMID:29033476

An efficient hybrid approach for multiobjective optimization of water distribution systems

NASA Astrophysics Data System (ADS)

Zheng, Feifei; Simpson, Angus R.; Zecchin, Aaron C.

2014-05-01

An efficient hybrid approach for the design of water distribution systems (WDSs) with multiple objectives is described in this paper. The objectives are the minimization of the network cost and maximization of the network resilience. A self-adaptive multiobjective differential evolution (SAMODE) algorithm has been developed, in which control parameters are automatically adapted by means of evolution instead of the presetting of fine-tuned parameter values. In the proposed method, a graph algorithm is first used to decompose a looped WDS into a shortest-distance tree (T) or forest, and chords (Ω). The original two-objective optimization problem is then approximated by a series of single-objective optimization problems of the T to be solved by nonlinear programming (NLP), thereby providing an approximate Pareto optimal front for the original whole network. Finally, the solutions at the approximate front are used to seed the SAMODE algorithm to find an improved front for the original entire network. The proposed approach is compared with two other conventional full-search optimization methods (the SAMODE algorithm and the NSGA-II) that seed the initial population with purely random solutions based on three case studies: a benchmark network and two real-world networks with multiple demand loading cases. Results show that (i) the proposed NLP-SAMODE method consistently generates better-quality Pareto fronts than the full-search methods with significantly improved efficiency; and (ii) the proposed SAMODE algorithm (no parameter tuning) exhibits better performance than the NSGA-II with calibrated parameter values in efficiently offering optimal fronts.

Efficient Approximation Algorithms for Weighted $b$-Matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khan, Arif; Pothen, Alex; Mostofa Ali Patwary, Md.

2016-01-01

We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a specified number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M. We prove that the b-Suitor algorithm computes the same b-Matching as the one obtained by the greedy algorithm for themore » problem. We implement the algorithm on serial and shared-memory parallel processors, and compare its performance against a collection of approximation algorithms that have been proposed for the Matching problem. Our results show that the b-Suitor algorithm outperforms the Greedy and Locally Dominant edge algorithms by one to two orders of magnitude on a serial processor. The b-Suitor algorithm has a high degree of concurrency, and it scales well up to 240 threads on a shared memory multiprocessor. The b-Suitor algorithm outperforms the Locally Dominant edge algorithm by a factor of fourteen on 16 cores of an Intel Xeon multiprocessor.« less

Mining and Indexing Graph Databases

ERIC Educational Resources Information Center

Yuan, Dayu

2013-01-01

Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…

Transforming graph states using single-qubit operations.

PubMed

Dahlberg, Axel; Wehner, Stephanie

2018-07-13

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. What is more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool-for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G ' is a vertex-minor of another graph G The vertex-minor problem is, in general, [Formula: see text]-Complete, but can be solved efficiently on graphs which are not too complex. A measure of the complexity of a graph is the rank-width which equals the Schmidt-rank width of a subclass of stabilizer states called graph states, and thus intuitively is a measure of entanglement. Here, we show that the vertex-minor problem can be solved in time O (| G | 3 ), where | G | is the size of the graph G , whenever the rank-width of G and the size of G ' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Short paths in expander graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kleinberg, J.; Rubinfeld, R.

Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the interconnection networks on which they run. We develop new routing algorithms and structural results for bounded-degree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work asserting that expanders are rich in short, disjoint paths. In particular, our work has consequences for the disjoint paths problem, multicommodify flow, and graph minor containment. We show: (i) A greedy algorithm for approximating the maximum disjoint paths problem achieves a polylogarithmic approximation ratiomore » in bounded-degree expanders. Although our algorithm is both deterministic and on-line, its performance guarantee is an improvement over previous bounds in expanders. (ii) For a multicommodily flow problem with arbitrary demands on a bounded-degree expander, there is a (1 + {epsilon})-optimal solution using only flow paths of polylogarithmic length. It follows that the multicommodity flow algorithm of Awerbuch and Leighton runs in nearly linear time per commodity in expanders. Our analysis is based on establishing the following: given edge weights on an expander G, one can increase some of the weights very slightly so the resulting shortest-path metric is smooth - the min-weight path between any pair of nodes uses a polylogarithmic number of edges. (iii) Every bounded-degree expander on n nodes contains every graph with O(n/log{sup O(1)} n) nodes and edges as a minor.« less

Reflections on High School Students' Graphing Skills and Their Conceptual Understanding of Drawing Chemistry Graphs

ERIC Educational Resources Information Center

Gültepe, Nejla

2016-01-01

Graphing subjects in chemistry has been used to provide alternatives to verbal and algorithmic descriptions of a subject by handing students another way of improving their manipulation of concepts. Teachers should therefore know the level of students' graphing skills. Studies have identified that students have difficulty making connections with…

Projections for fast protein structure retrieval

PubMed Central

Bhattacharya, Sourangshu; Bhattacharyya, Chiranjib; Chandra, Nagasuma R

2006-01-01

Background In recent times, there has been an exponential rise in the number of protein structures in databases e.g. PDB. So, design of fast algorithms capable of querying such databases is becoming an increasingly important research issue. This paper reports an algorithm, motivated from spectral graph matching techniques, for retrieving protein structures similar to a query structure from a large protein structure database. Each protein structure is specified by the 3D coordinates of residues of the protein. The algorithm is based on a novel characterization of the residues, called projections, leading to a similarity measure between the residues of the two proteins. This measure is exploited to efficiently compute the optimal equivalences. Results Experimental results show that, the current algorithm outperforms the state of the art on benchmark datasets in terms of speed without losing accuracy. Search results on SCOP 95% nonredundant database, for fold similarity with 5 proteins from different SCOP classes show that the current method performs competitively with the standard algorithm CE. The algorithm is also capable of detecting non-topological similarities between two proteins which is not possible with most of the state of the art tools like Dali. PMID:17254310

Discovering Authorities and Hubs in Different Topological Web Graph Structures.

ERIC Educational Resources Information Center

Meghabghab, George

2002-01-01

Discussion of citation analysis on the Web considers Web hyperlinks as a source to analyze citations. Topics include basic graph theory applied to Web pages, including matrices, linear algebra, and Web topology; and hubs and authorities, including a search technique called HITS (Hyperlink Induced Topic Search). (Author/LRW)

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, X; Belcher, AH; Wiersma, R

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimizationmore » and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

Maximal clique enumeration with data-parallel primitives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lessley, Brenton; Perciano, Talita; Mathai, Manish

The enumeration of all maximal cliques in an undirected graph is a fundamental problem arising in several research areas. We consider maximal clique enumeration on shared-memory, multi-core architectures and introduce an approach consisting entirely of data-parallel operations, in an effort to achieve efficient and portable performance across different architectures. We study the performance of the algorithm via experiments varying over benchmark graphs and architectures. Overall, we observe that our algorithm achieves up to a 33-time speedup and 9-time speedup over state-of-the-art distributed and serial algorithms, respectively, for graphs with higher ratios of maximal cliques to total cliques. Further, we attainmore » additional speedups on a GPU architecture, demonstrating the portable performance of our data-parallel design.« less

The parametric modified limited penetrable visibility graph for constructing complex networks from time series

NASA Astrophysics Data System (ADS)

Li, Xiuming; Sun, Mei; Gao, Cuixia; Han, Dun; Wang, Minggang

2018-02-01

This paper presents the parametric modified limited penetrable visibility graph (PMLPVG) algorithm for constructing complex networks from time series. We modify the penetrable visibility criterion of limited penetrable visibility graph (LPVG) in order to improve the rationality of the original penetrable visibility and preserve the dynamic characteristics of the time series. The addition of view angle provides a new approach to characterize the dynamic structure of the time series that is invisible in the previous algorithm. The reliability of the PMLPVG algorithm is verified by applying it to three types of artificial data as well as the actual data of natural gas prices in different regions. The empirical results indicate that PMLPVG algorithm can distinguish the different time series from each other. Meanwhile, the analysis results of natural gas prices data using PMLPVG are consistent with the detrended fluctuation analysis (DFA). The results imply that the PMLPVG algorithm may be a reasonable and significant tool for identifying various time series in different fields.

Ring system-based chemical graph generation for de novo molecular design

NASA Astrophysics Data System (ADS)

Miyao, Tomoyuki; Kaneko, Hiromasa; Funatsu, Kimito

2016-05-01

Generating chemical graphs in silico by combining building blocks is important and fundamental in virtual combinatorial chemistry. A premise in this area is that generated structures should be irredundant as well as exhaustive. In this study, we develop structure generation algorithms regarding combining ring systems as well as atom fragments. The proposed algorithms consist of three parts. First, chemical structures are generated through a canonical construction path. During structure generation, ring systems can be treated as reduced graphs having fewer vertices than those in the original ones. Second, diversified structures are generated by a simple rule-based generation algorithm. Third, the number of structures to be generated can be estimated with adequate accuracy without actual exhaustive generation. The proposed algorithms were implemented in structure generator Molgilla. As a practical application, Molgilla generated chemical structures mimicking rosiglitazone in terms of a two dimensional pharmacophore pattern. The strength of the algorithms lies in simplicity and flexibility. Therefore, they may be applied to various computer programs regarding structure generation by combining building blocks.

A Partitioning Algorithm for Block-Diagonal Matrices With Overlap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guy Antoine Atenekeng Kahou; Laura Grigori; Masha Sosonkina

2008-02-02

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile ismore » performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.« less

A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choudhury, Sutanay; Holder, Larry; Chin, George

2015-02-02

Cyber security is one of the most significant technical challenges in current times. Detecting adversarial activities, prevention of theft of intellectual properties and customer data is a high priority for corporations and government agencies around the world. Cyber defenders need to analyze massive-scale, high-resolution network flows to identify, categorize, and mitigate attacks involving net- works spanning institutional and national boundaries. Many of the cyber attacks can be described as subgraph patterns, with promi- nent examples being insider infiltrations (path queries), denial of service (parallel paths) and malicious spreads (tree queries). This motivates us to explore subgraph matching on streaming graphsmore » in a continuous setting. The novelty of our work lies in using the subgraph distributional statistics collected from the streaming graph to determine the query processing strategy. We introduce a “Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named “Relative Selectivity" that is used to se- lect between different query processing strategies. Our experiments performed on real online news, network traffic stream and a syn- thetic social network benchmark demonstrate 10-100x speedups over selectivity agnostic approaches.« less

Automatic MRI 2D brain segmentation using graph searching technique.

PubMed

Pedoia, Valentina; Binaghi, Elisabetta

2013-09-01

Accurate and efficient segmentation of the whole brain in magnetic resonance (MR) images is a key task in many neuroscience and medical studies either because the whole brain is the final anatomical structure of interest or because the automatic extraction facilitates further analysis. The problem of segmenting brain MRI images has been extensively addressed by many researchers. Despite the relevant achievements obtained, automated segmentation of brain MRI imagery is still a challenging problem whose solution has to cope with critical aspects such as anatomical variability and pathological deformation. In the present paper, we describe and experimentally evaluate a method for segmenting brain from MRI images basing on two-dimensional graph searching principles for border detection. The segmentation of the whole brain over the entire volume is accomplished slice by slice, automatically detecting frames including eyes. The method is fully automatic and easily reproducible by computing the internal main parameters directly from the image data. The segmentation procedure is conceived as a tool of general applicability, although design requirements are especially commensurate with the accuracy required in clinical tasks such as surgical planning and post-surgical assessment. Several experiments were performed to assess the performance of the algorithm on a varied set of MRI images obtaining good results in terms of accuracy and stability. Copyright © 2012 John Wiley & Sons, Ltd.

FacetGist: Collective Extraction of Document Facets in Large Technical Corpora.

PubMed

Siddiqui, Tarique; Ren, Xiang; Parameswaran, Aditya; Han, Jiawei

2016-10-01

Given the large volume of technical documents available, it is crucial to automatically organize and categorize these documents to be able to understand and extract value from them. Towards this end, we introduce a new research problem called Facet Extraction. Given a collection of technical documents, the goal of Facet Extraction is to automatically label each document with a set of concepts for the key facets ( e.g. , application, technique, evaluation metrics, and dataset) that people may be interested in. Facet Extraction has numerous applications, including document summarization, literature search, patent search and business intelligence. The major challenge in performing Facet Extraction arises from multiple sources: concept extraction, concept to facet matching, and facet disambiguation. To tackle these challenges, we develop FacetGist, a framework for facet extraction. Facet Extraction involves constructing a graph-based heterogeneous network to capture information available across multiple local sentence-level features, as well as global context features. We then formulate a joint optimization problem, and propose an efficient algorithm for graph-based label propagation to estimate the facet of each concept mention. Experimental results on technical corpora from two domains demonstrate that Facet Extraction can lead to an improvement of over 25% in both precision and recall over competing schemes.

FacetGist: Collective Extraction of Document Facets in Large Technical Corpora

PubMed Central

Siddiqui, Tarique; Ren, Xiang; Parameswaran, Aditya; Han, Jiawei

2017-01-01

Given the large volume of technical documents available, it is crucial to automatically organize and categorize these documents to be able to understand and extract value from them. Towards this end, we introduce a new research problem called Facet Extraction. Given a collection of technical documents, the goal of Facet Extraction is to automatically label each document with a set of concepts for the key facets (e.g., application, technique, evaluation metrics, and dataset) that people may be interested in. Facet Extraction has numerous applications, including document summarization, literature search, patent search and business intelligence. The major challenge in performing Facet Extraction arises from multiple sources: concept extraction, concept to facet matching, and facet disambiguation. To tackle these challenges, we develop FacetGist, a framework for facet extraction. Facet Extraction involves constructing a graph-based heterogeneous network to capture information available across multiple local sentence-level features, as well as global context features. We then formulate a joint optimization problem, and propose an efficient algorithm for graph-based label propagation to estimate the facet of each concept mention. Experimental results on technical corpora from two domains demonstrate that Facet Extraction can lead to an improvement of over 25% in both precision and recall over competing schemes. PMID:28210517

Extracting Knowledge from Graph Data in Adversarial Settings

NASA Astrophysics Data System (ADS)

Skillicorn, David

Graph data captures connections and relationships among individuals, and between individuals and objects, places, and times. Because many of the properties f graphs are emergent, they are resistant to manipulation by adversaries. This robustness comes at the expense of more-complex analysis algorithms. We describe several approaches to analysing graph data, illustrating with examples from the relationships within al Qaeda.

Many-core graph analytics using accelerated sparse linear algebra routines

NASA Astrophysics Data System (ADS)

Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

2016-05-01

Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

Multiple sclerosis lesion segmentation using an automatic multimodal graph cuts.

PubMed

García-Lorenzo, Daniel; Lecoeur, Jeremy; Arnold, Douglas L; Collins, D Louis; Barillot, Christian

2009-01-01

Graph Cuts have been shown as a powerful interactive segmentation technique in several medical domains. We propose to automate the Graph Cuts in order to automatically segment Multiple Sclerosis (MS) lesions in MRI. We replace the manual interaction with a robust EM-based approach in order to discriminate between MS lesions and the Normal Appearing Brain Tissues (NABT). Evaluation is performed in synthetic and real images showing good agreement between the automatic segmentation and the target segmentation. We compare our algorithm with the state of the art techniques and with several manual segmentations. An advantage of our algorithm over previously published ones is the possibility to semi-automatically improve the segmentation due to the Graph Cuts interactive feature.

Multifractal analysis of multiparticle emission data in the framework of visibility graph and sandbox algorithm

NASA Astrophysics Data System (ADS)

Mali, P.; Manna, S. K.; Mukhopadhyay, A.; Haldar, P. K.; Singh, G.

2018-03-01

Multiparticle emission data in nucleus-nucleus collisions are studied in a graph theoretical approach. The sandbox algorithm used to analyze complex networks is employed to characterize the multifractal properties of the visibility graphs associated with the pseudorapidity distribution of charged particles produced in high-energy heavy-ion collisions. Experimental data on 28Si+Ag/Br interaction at laboratory energy Elab = 14 . 5 A GeV, and 16O+Ag/Br and 32S+Ag/Br interactions both at Elab = 200 A GeV, are used in this analysis. We observe a scale free nature of the degree distributions of the visibility and horizontal visibility graphs associated with the event-wise pseudorapidity distributions. Equivalent event samples simulated by ultra-relativistic quantum molecular dynamics, produce degree distributions that are almost identical to the respective experiment. However, the multifractal variables obtained by using sandbox algorithm for the experiment to some extent differ from the respective simulated results.

Approximate ground states of the random-field Potts model from graph cuts

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

2018-05-01

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

NASA Astrophysics Data System (ADS)

Chen, Jung-Chieh

This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

Applied Graph-Mining Algorithms to Study Biomolecular Interaction Networks

PubMed Central

2014-01-01

Protein-protein interaction (PPI) networks carry vital information on the organization of molecular interactions in cellular systems. The identification of functionally relevant modules in PPI networks is one of the most important applications of biological network analysis. Computational analysis is becoming an indispensable tool to understand large-scale biomolecular interaction networks. Several types of computational methods have been developed and employed for the analysis of PPI networks. Of these computational methods, graph comparison and module detection are the two most commonly used strategies. This review summarizes current literature on graph kernel and graph alignment methods for graph comparison strategies, as well as module detection approaches including seed-and-extend, hierarchical clustering, optimization-based, probabilistic, and frequent subgraph methods. Herein, we provide a comprehensive review of the major algorithms employed under each theme, including our recently published frequent subgraph method, for detecting functional modules commonly shared across multiple cancer PPI networks. PMID:24800226

Fault-tolerant dynamic task graph scheduling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurt, Mehmet C.; Krishnamoorthy, Sriram; Agrawal, Kunal

2014-11-16

In this paper, we present an approach to fault tolerant execution of dynamic task graphs scheduled using work stealing. In particular, we focus on selective and localized recovery of tasks in the presence of soft faults. We elicit from the user the basic task graph structure in terms of successor and predecessor relationships. The work stealing-based algorithm to schedule such a task graph is augmented to enable recovery when the data and meta-data associated with a task get corrupted. We use this redundancy, and the knowledge of the task graph structure, to selectively recover from faults with low space andmore » time overheads. We show that the fault tolerant design retains the essential properties of the underlying work stealing-based task scheduling algorithm, and that the fault tolerant execution is asymptotically optimal when task re-execution is taken into account. Experimental evaluation demonstrates the low cost of recovery under various fault scenarios.« less

Projected power iteration for network alignment

NASA Astrophysics Data System (ADS)

Onaran, Efe; Villar, Soledad

2017-08-01

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erd-s-Renyí graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

Mining chemical reactions using neighborhood behavior and condensed graphs of reactions approaches.

PubMed

de Luca, Aurélie; Horvath, Dragos; Marcou, Gilles; Solov'ev, Vitaly; Varnek, Alexandre

2012-09-24

This work addresses the problem of similarity search and classification of chemical reactions using Neighborhood Behavior (NB) and Condensed Graphs of Reaction (CGR) approaches. The CGR formalism represents chemical reactions as a classical molecular graph with dynamic bonds, enabling descriptor calculations on this graph. Different types of the ISIDA fragment descriptors generated for CGRs in combination with two metrics--Tanimoto and Euclidean--were considered as chemical spaces, to serve for reaction dissimilarity scoring. The NB method has been used to select an optimal combination of descriptors which distinguish different types of chemical reactions in a database containing 8544 reactions of 9 classes. Relevance of NB analysis has been validated in generic (multiclass) similarity search and in clustering with Self-Organizing Maps (SOM). NB-compliant sets of descriptors were shown to display enhanced mapping propensities, allowing the construction of better Self-Organizing Maps and similarity searches (NB and classical similarity search criteria--AUC ROC--correlate at a level of 0.7). The analysis of the SOM clusters proved chemically meaningful CGR substructures representing specific reaction signatures.

Graph-drawing algorithms geometries versus molecular mechanics in fullereness

NASA Astrophysics Data System (ADS)

Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

1996-09-01

The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE PAGES

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg; ...

2018-05-03

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Incremental isometric embedding of high-dimensional data using connected neighborhood graphs.

PubMed

Zhao, Dongfang; Yang, Li

2009-01-01

Most nonlinear data embedding methods use bottom-up approaches for capturing the underlying structure of data distributed on a manifold in high dimensional space. These methods often share the first step which defines neighbor points of every data point by building a connected neighborhood graph so that all data points can be embedded to a single coordinate system. These methods are required to work incrementally for dimensionality reduction in many applications. Because input data stream may be under-sampled or skewed from time to time, building connected neighborhood graph is crucial to the success of incremental data embedding using these methods. This paper presents algorithms for updating $k$-edge-connected and $k$-connected neighborhood graphs after a new data point is added or an old data point is deleted. It further utilizes a simple algorithm for updating all-pair shortest distances on the neighborhood graph. Together with incremental classical multidimensional scaling using iterative subspace approximation, this paper devises an incremental version of Isomap with enhancements to deal with under-sampled or unevenly distributed data. Experiments on both synthetic and real-world data sets show that the algorithm is efficient and maintains low dimensional configurations of high dimensional data under various data distributions.

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Coloring geographical threshold graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bradonjic, Milan; Percus, Allon; Muller, Tobias

We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyzemore » the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.« less

Kidney segmentation in CT sequences using graph cuts based active contours model and contextual continuity.

PubMed

Zhang, Pin; Liang, Yanmei; Chang, Shengjiang; Fan, Hailun

2013-08-01

Accurate segmentation of renal tissues in abdominal computed tomography (CT) image sequences is an indispensable step for computer-aided diagnosis and pathology detection in clinical applications. In this study, the goal is to develop a radiology tool to extract renal tissues in CT sequences for the management of renal diagnosis and treatments. In this paper, the authors propose a new graph-cuts-based active contours model with an adaptive width of narrow band for kidney extraction in CT image sequences. Based on graph cuts and contextual continuity, the segmentation is carried out slice-by-slice. In the first stage, the middle two adjacent slices in a CT sequence are segmented interactively based on the graph cuts approach. Subsequently, the deformable contour evolves toward the renal boundaries by the proposed model for the kidney extraction of the remaining slices. In this model, the energy function combining boundary with regional information is optimized in the constructed graph and the adaptive search range is determined by contextual continuity and the object size. In addition, in order to reduce the complexity of the min-cut computation, the nodes in the graph only have n-links for fewer edges. The total 30 CT images sequences with normal and pathological renal tissues are used to evaluate the accuracy and effectiveness of our method. The experimental results reveal that the average dice similarity coefficient of these image sequences is from 92.37% to 95.71% and the corresponding standard deviation for each dataset is from 2.18% to 3.87%. In addition, the average automatic segmentation time for one kidney in each slice is about 0.36 s. Integrating the graph-cuts-based active contours model with contextual continuity, the algorithm takes advantages of energy minimization and the characteristics of image sequences. The proposed method achieves effective results for kidney segmentation in CT sequences.

Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

1976, 212-223. 110] M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. 1111 , A theorem on matchings in the plane, Graph Theory...in Memory of G.A. Dirac, Ann. Discrete Math . 41, North-Holland, Amsterdam, 1989, 347-354. 1121 N. Sbihi, Algorithme de recherche d’un stable de...cardinalitA maximum dans un graphe sans 6toile, Discrete Math . 29, 1980, 53-76. 1131 D. Sumner, On Tutte’s factorization theorem, Graphs and Combinatorics

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

NASA Astrophysics Data System (ADS)

Zhou, Lifan; Chai, Dengfeng; Xia, Yu; Ma, Peifeng; Lin, Hui

2018-01-01

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

GraphReduce: Processing Large-Scale Graphs on Accelerator-Based Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil

2015-11-15

Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host andmore » device.« less

Fast Decentralized Averaging via Multi-scale Gossip

NASA Astrophysics Data System (ADS)

Tsianos, Konstantinos I.; Rabbat, Michael G.

We are interested in the problem of computing the average consensus in a distributed fashion on random geometric graphs. We describe a new algorithm called Multi-scale Gossip which employs a hierarchical decomposition of the graph to partition the computation into tractable sub-problems. Using only pairwise messages of fixed size that travel at most O(n^{1/3}) hops, our algorithm is robust and has communication cost of O(n loglogn logɛ - 1) transmissions, which is order-optimal up to the logarithmic factor in n. Simulated experiments verify the good expected performance on graphs of many thousands of nodes.

Iterative cross section sequence graph for handwritten character segmentation.

PubMed

Dawoud, Amer

2007-08-01

The iterative cross section sequence graph (ICSSG) is an algorithm for handwritten character segmentation. It expands the cross section sequence graph concept by applying it iteratively at equally spaced thresholds. The iterative thresholding reduces the effect of information loss associated with image binarization. ICSSG preserves the characters' skeletal structure by preventing the interference of pixels that causes flooding of adjacent characters' segments. Improving the structural quality of the characters' skeleton facilitates better feature extraction and classification, which improves the overall performance of optical character recognition (OCR). Experimental results showed significant improvements in OCR recognition rates compared to other well-established segmentation algorithms.

A graph-Laplacian-based feature extraction algorithm for neural spike sorting.

PubMed

Ghanbari, Yasser; Spence, Larry; Papamichalis, Panos

2009-01-01

Analysis of extracellular neural spike recordings is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering which is performed in the feature space. This paper proposes a new feature extraction method (which we call Graph Laplacian Features, GLF) based on minimizing the graph Laplacian and maximizing the weighted variance. The algorithm is compared with Principal Components Analysis (PCA, the most commonly-used feature extraction method) using simulated neural data. The results show that the proposed algorithm produces more compact and well-separated clusters compared to PCA. As an added benefit, tentative cluster centers are output which can be used to initialize a subsequent clustering stage.

Diagnostic and Remedial Learning Strategy Based on Conceptual Graphs

ERIC Educational Resources Information Center

Jong, BinShyan; Lin, TsongWuu; Wu, YuLung; Chan, Teyi

2004-01-01

Numerous scholars have applied conceptual graphs for explanatory purposes. This study devised the Remedial-Instruction Decisive path (RID path) algorithm for diagnosing individual student learning situation. This study focuses on conceptual graphs. According to the concepts learned by students and the weight values of relations among these…

Structure-guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm.

PubMed

Maximova, Tatiana; Plaku, Erion; Shehu, Amarda

2016-07-07

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

Reduced graphs and their applications in chemoinformatics.

PubMed

Birchall, Kristian; Gillet, Valerie J

2011-01-01

Reduced graphs provide summary representations of chemical structures by collapsing groups of connected atoms into single nodes while preserving the topology of the original structures. This chapter reviews the extensive work that has been carried out on reduced graphs at The University of Sheffield and includes discussion of their application to the representation and search of Markush structures in patents, the varied approaches that have been implemented for similarity searching, their use in cluster representation, the different ways in which they have been applied to extract structure-activity relationships and their use in encoding bioisosteres.

jCompoundMapper: An open source Java library and command-line tool for chemical fingerprints

PubMed Central

2011-01-01

Background The decomposition of a chemical graph is a convenient approach to encode information of the corresponding organic compound. While several commercial toolkits exist to encode molecules as so-called fingerprints, only a few open source implementations are available. The aim of this work is to introduce a library for exactly defined molecular decompositions, with a strong focus on the application of these features in machine learning and data mining. It provides several options such as search depth, distance cut-offs, atom- and pharmacophore typing. Furthermore, it provides the functionality to combine, to compare, or to export the fingerprints into several formats. Results We provide a Java 1.6 library for the decomposition of chemical graphs based on the open source Chemistry Development Kit toolkit. We reimplemented popular fingerprinting algorithms such as depth-first search fingerprints, extended connectivity fingerprints, autocorrelation fingerprints (e.g. CATS2D), radial fingerprints (e.g. Molprint2D), geometrical Molprint, atom pairs, and pharmacophore fingerprints. We also implemented custom fingerprints such as the all-shortest path fingerprint that only includes the subset of shortest paths from the full set of paths of the depth-first search fingerprint. As an application of jCompoundMapper, we provide a command-line executable binary. We measured the conversion speed and number of features for each encoding and described the composition of the features in detail. The quality of the encodings was tested using the default parametrizations in combination with a support vector machine on the Sutherland QSAR data sets. Additionally, we benchmarked the fingerprint encodings on the large-scale Ames toxicity benchmark using a large-scale linear support vector machine. The results were promising and could often compete with literature results. On the large Ames benchmark, for example, we obtained an AUC ROC performance of 0.87 with a reimplementation of the extended connectivity fingerprint. This result is comparable to the performance achieved by a non-linear support vector machine using state-of-the-art descriptors. On the Sutherland QSAR data set, the best fingerprint encodings showed a comparable or better performance on 5 of the 8 benchmarks when compared against the results of the best descriptors published in the paper of Sutherland et al. Conclusions jCompoundMapper is a library for chemical graph fingerprints with several tweaking possibilities and exporting options for open source data mining toolkits. The quality of the data mining results, the conversion speed, the LPGL software license, the command-line interface, and the exporters should be useful for many applications in cheminformatics like benchmarks against literature methods, comparison of data mining algorithms, similarity searching, and similarity-based data mining. PMID:21219648

An Integrated Approach to Locality-Conscious Processor Allocation and Scheduling of Mixed-Parallel Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vydyanathan, Naga; Krishnamoorthy, Sriram; Sabin, Gerald M.

2009-08-01

Complex parallel applications can often be modeled as directed acyclic graphs of coarse-grained application-tasks with dependences. These applications exhibit both task- and data-parallelism, and combining these two (also called mixedparallelism), has been shown to be an effective model for their execution. In this paper, we present an algorithm to compute the appropriate mix of task- and data-parallelism required to minimize the parallel completion time (makespan) of these applications. In other words, our algorithm determines the set of tasks that should be run concurrently and the number of processors to be allocated to each task. The processor allocation and scheduling decisionsmore » are made in an integrated manner and are based on several factors such as the structure of the taskgraph, the runtime estimates and scalability characteristics of the tasks and the inter-task data communication volumes. A locality conscious scheduling strategy is used to improve inter-task data reuse. Evaluation through simulations and actual executions of task graphs derived from real applications as well as synthetic graphs shows that our algorithm consistently generates schedules with lower makespan as compared to CPR and CPA, two previously proposed scheduling algorithms. Our algorithm also produces schedules that have lower makespan than pure taskand data-parallel schedules. For task graphs with known optimal schedules or lower bounds on the makespan, our algorithm generates schedules that are closer to the optima than other scheduling approaches.« less

GIRAF: a method for fast search and flexible alignment of ligand binding interfaces in proteins at atomic resolution

PubMed Central

Kinjo, Akira R.; Nakamura, Haruki

2012-01-01

Comparison and classification of protein structures are fundamental means to understand protein functions. Due to the computational difficulty and the ever-increasing amount of structural data, however, it is in general not feasible to perform exhaustive all-against-all structure comparisons necessary for comprehensive classifications. To efficiently handle such situations, we have previously proposed a method, now called GIRAF. We herein describe further improvements in the GIRAF protein structure search and alignment method. The GIRAF method achieves extremely efficient search of similar structures of ligand binding sites of proteins by exploiting database indexing of structural features of local coordinate frames. In addition, it produces refined atom-wise alignments by iterative applications of the Hungarian method to the bipartite graph defined for a pair of superimposed structures. By combining the refined alignments based on different local coordinate frames, it is made possible to align structures involving domain movements. We provide detailed accounts for the database design, the search and alignment algorithms as well as some benchmark results. PMID:27493524

Literature Search through Mixed-Membership Community Discovery

NASA Astrophysics Data System (ADS)

Eliassi-Rad, Tina; Henderson, Keith

We introduce a new approach to literature search that is based on finding mixed-membership communities on an augmented co-authorship graph (ACA) with a scalable generative model. An ACA graph contains two types of edges: (1) coauthorship links and (2) links between researchers with substantial expertise overlap. Our solution eliminates the biases introduced by either looking at citations of a paper or doing a Web search. A case study on PubMed shows the benefits of our approach.

Automatic segmentation of nine retinal layer boundaries in OCT images of non-exudative AMD patients using deep learning and graph search

PubMed Central

Fang, Leyuan; Cunefare, David; Wang, Chong; Guymer, Robyn H.; Li, Shutao; Farsiu, Sina

2017-01-01

We present a novel framework combining convolutional neural networks (CNN) and graph search methods (termed as CNN-GS) for the automatic segmentation of nine layer boundaries on retinal optical coherence tomography (OCT) images. CNN-GS first utilizes a CNN to extract features of specific retinal layer boundaries and train a corresponding classifier to delineate a pilot estimate of the eight layers. Next, a graph search method uses the probability maps created from the CNN to find the final boundaries. We validated our proposed method on 60 volumes (2915 B-scans) from 20 human eyes with non-exudative age-related macular degeneration (AMD), which attested to effectiveness of our proposed technique. PMID:28663902

Automatic segmentation of nine retinal layer boundaries in OCT images of non-exudative AMD patients using deep learning and graph search.

PubMed

Fang, Leyuan; Cunefare, David; Wang, Chong; Guymer, Robyn H; Li, Shutao; Farsiu, Sina

2017-05-01

We present a novel framework combining convolutional neural networks (CNN) and graph search methods (termed as CNN-GS) for the automatic segmentation of nine layer boundaries on retinal optical coherence tomography (OCT) images. CNN-GS first utilizes a CNN to extract features of specific retinal layer boundaries and train a corresponding classifier to delineate a pilot estimate of the eight layers. Next, a graph search method uses the probability maps created from the CNN to find the final boundaries. We validated our proposed method on 60 volumes (2915 B-scans) from 20 human eyes with non-exudative age-related macular degeneration (AMD), which attested to effectiveness of our proposed technique.

Quantum snake walk on graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosmanis, Ansis

2011-02-15

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, whichmore » asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.« less

Simulator for heterogeneous dataflow architectures

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

1993-01-01

A new simulator is developed to simulate the execution of an algorithm graph in accordance with the Algorithm to Architecture Mapping Model (ATAMM) rules. ATAMM is a Petri Net model which describes the periodic execution of large-grained, data-independent dataflow graphs and which provides predictable steady state time-optimized performance. This simulator extends the ATAMM simulation capability from a heterogenous set of resources, or functional units, to a more general heterogenous architecture. Simulation test cases show that the simulator accurately executes the ATAMM rules for both a heterogenous architecture and a homogenous architecture, which is the special case for only one processor type. The simulator forms one tool in an ATAMM Integrated Environment which contains other tools for graph entry, graph modification for performance optimization, and playback of simulations for analysis.

Two criteria for the selection of assembly plans - Maximizing the flexibility of sequencing the assembly tasks and minimizing the assembly time through parallel execution of assembly tasks

NASA Technical Reports Server (NTRS)

Homem De Mello, Luiz S.; Sanderson, Arthur C.

1991-01-01

The authors introduce two criteria for the evaluation and selection of assembly plans. The first criterion is to maximize the number of different sequences in which the assembly tasks can be executed. The second criterion is to minimize the total assembly time through simultaneous execution of assembly tasks. An algorithm that performs a heuristic search for the best assembly plan over the AND/OR graph representation of assembly plans is discussed. Admissible heuristics for each of the two criteria introduced are presented. Some implementation issues that affect the computational efficiency are addressed.

The Roadmaker's algorithm for the discrete pulse transform.

PubMed

Laurie, Dirk P

2011-02-01

The discrete pulse transform (DPT) is a decomposition of an observed signal into a sum of pulses, i.e., signals that are constant on a connected set and zero elsewhere. Originally developed for 1-D signal processing, the DPT has recently been generalized to more dimensions. Applications in image processing are currently being investigated. The time required to compute the DPT as originally defined via the successive application of LULU operators (members of a class of minimax filters studied by Rohwer) has been a severe drawback to its applicability. This paper introduces a fast method for obtaining such a decomposition, called the Roadmaker's algorithm because it involves filling pits and razing bumps. It acts selectively only on those features actually present in the signal, flattening them in order of increasing size by subtracing an appropriate positive or negative pulse, which is then appended to the decomposition. The implementation described here covers 1-D signal as well as two and 3-D image processing in a single framework. This is achieved by considering the signal or image as a function defined on a graph, with the geometry specified by the edges of the graph. Whenever a feature is flattened, nodes in the graph are merged, until eventually only one node remains. At that stage, a new set of edges for the same nodes as the graph, forming a tree structure, defines the obtained decomposition. The Roadmaker's algorithm is shown to be equivalent to the DPT in the sense of obtaining the same decomposition. However, its simpler operators are not in general equivalent to the LULU operators in situations where those operators are not applied successively. A by-product of the Roadmaker's algorithm is that it yields a proof of the so-called Highlight Conjecture, stated as an open problem in 2006. We pay particular attention to algorithmic details and complexity, including a demonstration that in the 1-D case, and also in the case of a complete graph, the Roadmaker's algorithm has optimal complexity: it runs in time O(m), where m is the number of arcs in the graph.

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing.

PubMed

Altarelli, Fabrizio; Braunstein, Alfredo; Dall'Asta, Luca; De Bacco, Caterina; Franz, Silvio

2015-01-01

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length.

Eigenvector synchronization, graph rigidity and the molecule problemR

PubMed Central

Cucuringu, Mihai; Singer, Amit; Cowburn, David

2013-01-01

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend the previous work and propose the 3D-As-Synchronized-As-Possible (3D-ASAP) algorithm, for the graph realization problem in ℝ3, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch, there corresponds an element of the Euclidean group, Euc(3), of rigid transformations in ℝ3, and the goal was to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-spectral-partitioning (SP)-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a pre-processing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably with similar state-of-the-art localization algorithms. PMID:24432187

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

PubMed Central

2015-01-01

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length. PMID:26710102

Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

interac- tive image segmentation using the solution to a combinatorial Dirichlet problem. Elmoataz et al . have developed general- izations of the graph...Laplacian [25] for image denoising and manifold smoothing. Couprie et al . in [18] define a conve- niently parameterized graph-based energy function that...over to the discrete graph representation. For general data segmentation, Bresson et al . in [8], present rigorous convergence results for two algorithms

GraphReduce: Large-Scale Graph Analytics on Accelerator-Based HPC Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen

2015-09-30

Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of both edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the hostmore » and the device.« less

Attributed relational graphs for cell nucleus segmentation in fluorescence microscopy images.

PubMed

Arslan, Salim; Ersahin, Tulin; Cetin-Atalay, Rengul; Gunduz-Demir, Cigdem

2013-06-01

More rapid and accurate high-throughput screening in molecular cellular biology research has become possible with the development of automated microscopy imaging, for which cell nucleus segmentation commonly constitutes the core step. Although several promising methods exist for segmenting the nuclei of monolayer isolated and less-confluent cells, it still remains an open problem to segment the nuclei of more-confluent cells, which tend to grow in overlayers. To address this problem, we propose a new model-based nucleus segmentation algorithm. This algorithm models how a human locates a nucleus by identifying the nucleus boundaries and piecing them together. In this algorithm, we define four types of primitives to represent nucleus boundaries at different orientations and construct an attributed relational graph on the primitives to represent their spatial relations. Then, we reduce the nucleus identification problem to finding predefined structural patterns in the constructed graph and also use the primitives in region growing to delineate the nucleus borders. Working with fluorescence microscopy images, our experiments demonstrate that the proposed algorithm identifies nuclei better than previous nucleus segmentation algorithms.

Finding Hierarchical and Overlapping Dense Subgraphs using Nucleus Decompositions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seshadhri, Comandur; Pinar, Ali; Sariyuce, Ahmet Erdem

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique, k-densest subgraph) are NP-hard. Furthermore, the goal is rarely to nd the \\true optimum", but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine a hierarchical structure among them. Current dense subgraph nding algorithms usually optimize some objective, and only nd a few such subgraphs without providing any hierarchy. It is also not clear how to account formore » overlaps in dense substructures. We de ne the nucleus decomposition of a graph, which represents the graph as a forest of nuclei. Each nucleus is a subgraph where smaller cliques are present in many larger cliques. The forest of nuclei is a hierarchy by containment, where the edge density increases as we proceed towards leaf nuclei. Sibling nuclei can have limited intersections, which allows for discovery of overlapping dense subgraphs. With the right parameters, the nuclear decomposition generalizes the classic notions of k-cores and k-trusses. We give provable e cient algorithms for nuclear decompositions, and empirically evaluate their behavior in a variety of real graphs. The tree of nuclei consistently gives a global, hierarchical snapshot of dense substructures, and outputs dense subgraphs of higher quality than other state-of-theart solutions. Our algorithm can process graphs with tens of millions of edges in less than an hour.« less

Predicting and Detecting Emerging Cyberattack Patterns Using StreamWorks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chin, George; Choudhury, Sutanay; Feo, John T.

2014-06-30

The number and sophistication of cyberattacks on industries and governments have dramatically grown in recent years. To counter this movement, new advanced tools and techniques are needed to detect cyberattacks in their early stages such that defensive actions may be taken to avert or mitigate potential damage. From a cybersecurity analysis perspective, detecting cyberattacks may be cast as a problem of identifying patterns in computer network traffic. Logically and intuitively, these patterns may take on the form of a directed graph that conveys how an attack or intrusion propagates through the computers of a network. Such cyberattack graphs could providemore » cybersecurity analysts with powerful conceptual representations that are natural to express and analyze. We have been researching and developing graph-centric approaches and algorithms for dynamic cyberattack detection. The advanced dynamic graph algorithms we are developing will be packaged into a streaming network analysis framework known as StreamWorks. With StreamWorks, a scientist or analyst may detect and identify precursor events and patterns as they emerge in complex networks. This analysis framework is intended to be used in a dynamic environment where network data is streamed in and is appended to a large-scale dynamic graph. Specific graphical query patterns are decomposed and collected into a graph query library. The individual decomposed subpatterns in the library are continuously and efficiently matched against the dynamic graph as it evolves to identify and detect early, partial subgraph patterns. The scalable emerging subgraph pattern algorithms will match on both structural and semantic network properties.« less

Attribute-based Decision Graphs: A framework for multiclass data classification.

PubMed

Bertini, João Roberto; Nicoletti, Maria do Carmo; Zhao, Liang

2017-01-01

Graph-based algorithms have been successfully applied in machine learning and data mining tasks. A simple but, widely used, approach to build graphs from vector-based data is to consider each data instance as a vertex and connecting pairs of it using a similarity measure. Although this abstraction presents some advantages, such as arbitrary shape representation of the original data, it is still tied to some drawbacks, for example, it is dependent on the choice of a pre-defined distance metric and is biased by the local information among data instances. Aiming at exploring alternative ways to build graphs from data, this paper proposes an algorithm for constructing a new type of graph, called Attribute-based Decision Graph-AbDG. Given a vector-based data set, an AbDG is built by partitioning each data attribute range into disjoint intervals and representing each interval as a vertex. The edges are then established between vertices from different attributes according to a pre-defined pattern. Classification is performed through a matching process among the attribute values of the new instance and AbDG. Moreover, AbDG provides an inner mechanism to handle missing attribute values, which contributes for expanding its applicability. Results of classification tasks have shown that AbDG is a competitive approach when compared to well-known multiclass algorithms. The main contribution of the proposed framework is the combination of the advantages of attribute-based and graph-based techniques to perform robust pattern matching data classification, while permitting the analysis the input data considering only a subset of its attributes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain.

PubMed

Pang, Jiahao; Cheung, Gene

2017-04-01

Inverse imaging problems are inherently underdetermined, and hence, it is important to employ appropriate image priors for regularization. One recent popular prior-the graph Laplacian regularizer-assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods, such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

Markovian Search Games in Heterogeneous Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

2009-01-01

We consider how to search for a mobile evader in a large heterogeneous region when sensors are used for detection. Sensors are modeled using probability of detection. Due to environmental effects, this probability will not be constant over the entire region. We map this problem to a graph search problem and, even though deterministic graph search is NP-complete, we derive a tractable, optimal, probabilistic search strategy. We do this by defining the problem as a differential game played on a Markov chain. We prove that this strategy is optimal in the sense of Nash. Simulations of an example problem illustratemore » our approach and verify our claims.« less

GraphStore: A Distributed Graph Storage System for Big Data Networks

ERIC Educational Resources Information Center

Martha, VenkataSwamy

2013-01-01

Networks, such as social networks, are a universal solution for modeling complex problems in real time, especially in the Big Data community. While previous studies have attempted to enhance network processing algorithms, none have paved a path for the development of a persistent storage system. The proposed solution, GraphStore, provides an…

Graph rigidity, cyclic belief propagation, and point pattern matching.

PubMed

McAuley, Julian J; Caetano, Tibério S; Barbosa, Marconi S

2008-11-01

A recent paper [1] proposed a provably optimal polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be globally rigid, implying that exact inference provides the same matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph that is also globally rigid but has an advantage over the graph proposed in [1]: Its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal, and thus, standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that in [1] when there is noise in the point patterns.

Exact numerical calculation of fixation probability and time on graphs.

PubMed

Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt

2016-12-01

The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Listing triangles in expected linear time on a class of power law graphs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann

Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysismore » for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.« less

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

An Algorithm to Automatically Generate the Combinatorial Orbit Counting Equations

PubMed Central

Melckenbeeck, Ine; Audenaert, Pieter; Michoel, Tom; Colle, Didier; Pickavet, Mario

2016-01-01

Graphlets are small subgraphs, usually containing up to five vertices, that can be found in a larger graph. Identification of the graphlets that a vertex in an explored graph touches can provide useful information about the local structure of the graph around that vertex. Actually finding all graphlets in a large graph can be time-consuming, however. As the graphlets grow in size, more different graphlets emerge and the time needed to find each graphlet also scales up. If it is not needed to find each instance of each graphlet, but knowing the number of graphlets touching each node of the graph suffices, the problem is less hard. Previous research shows a way to simplify counting the graphlets: instead of looking for the graphlets needed, smaller graphlets are searched, as well as the number of common neighbors of vertices. Solving a system of equations then gives the number of times a vertex is part of each graphlet of the desired size. However, until now, equations only exist to count graphlets with 4 or 5 nodes. In this paper, two new techniques are presented. The first allows to generate the equations needed in an automatic way. This eliminates the tedious work needed to do so manually each time an extra node is added to the graphlets. The technique is independent on the number of nodes in the graphlets and can thus be used to count larger graphlets than previously possible. The second technique gives all graphlets a unique ordering which is easily extended to name graphlets of any size. Both techniques were used to generate equations to count graphlets with 4, 5 and 6 vertices, which extends all previous results. Code can be found at https://github.com/IneMelckenbeeck/equation-generator and https://github.com/IneMelckenbeeck/graphlet-naming. PMID:26797021

Knowledge-based understanding of aerial surveillance video

NASA Astrophysics Data System (ADS)

Cheng, Hui; Butler, Darren

2006-05-01

Aerial surveillance has long been used by the military to locate, monitor and track the enemy. Recently, its scope has expanded to include law enforcement activities, disaster management and commercial applications. With the ever-growing amount of aerial surveillance video acquired daily, there is an urgent need for extracting actionable intelligence in a timely manner. Furthermore, to support high-level video understanding, this analysis needs to go beyond current approaches and consider the relationships, motivations and intentions of the objects in the scene. In this paper we propose a system for interpreting aerial surveillance videos that automatically generates a succinct but meaningful description of the observed regions, objects and events. For a given video, the semantics of important regions and objects, and the relationships between them, are summarised into a semantic concept graph. From this, a textual description is derived that provides new search and indexing options for aerial video and enables the fusion of aerial video with other information modalities, such as human intelligence, reports and signal intelligence. Using a Mixture-of-Experts video segmentation algorithm an aerial video is first decomposed into regions and objects with predefined semantic meanings. The objects are then tracked and coerced into a semantic concept graph and the graph is summarized spatially, temporally and semantically using ontology guided sub-graph matching and re-writing. The system exploits domain specific knowledge and uses a reasoning engine to verify and correct the classes, identities and semantic relationships between the objects. This approach is advantageous because misclassifications lead to knowledge contradictions and hence they can be easily detected and intelligently corrected. In addition, the graph representation highlights events and anomalies that a low-level analysis would overlook.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

QSPIN: A High Level Java API for Quantum Computing Experimentation

NASA Technical Reports Server (NTRS)

Barth, Tim

2017-01-01

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

Parallel Algorithms for Switching Edges in Heterogeneous Graphs☆

PubMed Central

Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

2017-01-01

An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors. PMID:28757680

A graph-based evolutionary algorithm: Genetic Network Programming (GNP) and its extension using reinforcement learning.

PubMed

Mabu, Shingo; Hirasawa, Kotaro; Hu, Jinglu

2007-01-01

This paper proposes a graph-based evolutionary algorithm called Genetic Network Programming (GNP). Our goal is to develop GNP, which can deal with dynamic environments efficiently and effectively, based on the distinguished expression ability of the graph (network) structure. The characteristics of GNP are as follows. 1) GNP programs are composed of a number of nodes which execute simple judgment/processing, and these nodes are connected by directed links to each other. 2) The graph structure enables GNP to re-use nodes, thus the structure can be very compact. 3) The node transition of GNP is executed according to its node connections without any terminal nodes, thus the past history of the node transition affects the current node to be used and this characteristic works as an implicit memory function. These structural characteristics are useful for dealing with dynamic environments. Furthermore, we propose an extended algorithm, "GNP with Reinforcement Learning (GNPRL)" which combines evolution and reinforcement learning in order to create effective graph structures and obtain better results in dynamic environments. In this paper, we applied GNP to the problem of determining agents' behavior to evaluate its effectiveness. Tileworld was used as the simulation environment. The results show some advantages for GNP over conventional methods.

Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data.

PubMed

Dong, Jianwu; Chen, Feng; Zhou, Dong; Liu, Tian; Yu, Zhaofei; Wang, Yi

2017-03-01

Existence of low SNR regions and rapid-phase variations pose challenges to spatial phase unwrapping algorithms. Global optimization-based phase unwrapping methods are widely used, but are significantly slower than greedy methods. In this paper, dual decomposition acceleration is introduced to speed up a three-dimensional graph cut-based phase unwrapping algorithm. The phase unwrapping problem is formulated as a global discrete energy minimization problem, whereas the technique of dual decomposition is used to increase the computational efficiency by splitting the full problem into overlapping subproblems and enforcing the congruence of overlapping variables. Using three dimensional (3D) multiecho gradient echo images from an agarose phantom and five brain hemorrhage patients, we compared this proposed method with an unaccelerated graph cut-based method. Experimental results show up to 18-fold acceleration in computation time. Dual decomposition significantly improves the computational efficiency of 3D graph cut-based phase unwrapping algorithms. Magn Reson Med 77:1353-1358, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Information Dynamics in Networks: Models and Algorithms

DTIC Science & Technology

2016-09-13

Twitter ; we investigated how to detect spam accounts on Facebook and other social networks by graph analytics; and finally we investigated how to design...networks. We investigated the appropriateness of existing mathematical models for explaining the structure of retweet cascades on Twitter ; we investigated...Received Paper 1.00 2.00 3.00 . A Note on Modeling Retweet Cascades on Twitter , Workshop on Algorithms and Models for the Web Graph. 09-DEC-15

Applying graph partitioning methods in measurement-based dynamic load balancing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhatele, Abhinav; Fourestier, Sebastien; Menon, Harshitha

Load imbalance leads to an increasing waste of resources as an application is scaled to more and more processors. Achieving the best parallel efficiency for a program requires optimal load balancing which is a NP-hard problem. However, finding near-optimal solutions to this problem for complex computational science and engineering applications is becoming increasingly important. Charm++, a migratable objects based programming model, provides a measurement-based dynamic load balancing framework. This framework instruments and then migrates over-decomposed objects to balance computational load and communication at runtime. This paper explores the use of graph partitioning algorithms, traditionally used for partitioning physical domains/meshes, formore » measurement-based dynamic load balancing of parallel applications. In particular, we present repartitioning methods developed in a graph partitioning toolbox called SCOTCH that consider the previous mapping to minimize migration costs. We also discuss a new imbalance reduction algorithm for graphs with irregular load distributions. We compare several load balancing algorithms using microbenchmarks on Intrepid and Ranger and evaluate the effect of communication, number of cores and number of objects on the benefit achieved from load balancing. New algorithms developed in SCOTCH lead to better performance compared to the METIS partitioners for several cases, both in terms of the application execution time and fewer number of objects migrated.« less

Task scheduling in dataflow computer architectures

NASA Technical Reports Server (NTRS)

Katsinis, Constantine

1994-01-01

Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.

Diverse task scheduling for individualized requirements in cloud manufacturing

NASA Astrophysics Data System (ADS)

Zhou, Longfei; Zhang, Lin; Zhao, Chun; Laili, Yuanjun; Xu, Lida

2018-03-01

Cloud manufacturing (CMfg) has emerged as a new manufacturing paradigm that provides ubiquitous, on-demand manufacturing services to customers through network and CMfg platforms. In CMfg system, task scheduling as an important means of finding suitable services for specific manufacturing tasks plays a key role in enhancing the system performance. Customers' requirements in CMfg are highly individualized, which leads to diverse manufacturing tasks in terms of execution flows and users' preferences. We focus on diverse manufacturing tasks and aim to address their scheduling issue in CMfg. First of all, a mathematical model of task scheduling is built based on analysis of the scheduling process in CMfg. To solve this scheduling problem, we propose a scheduling method aiming for diverse tasks, which enables each service demander to obtain desired manufacturing services. The candidate service sets are generated according to subtask directed graphs. An improved genetic algorithm is applied to searching for optimal task scheduling solutions. The effectiveness of the scheduling method proposed is verified by a case study with individualized customers' requirements. The results indicate that the proposed task scheduling method is able to achieve better performance than some usual algorithms such as simulated annealing and pattern search.

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression

PubMed Central

Fasmer, Erlend Eindride; Berle, Jan Øystein; Oedegaard, Ketil J.; Hauge, Erik R.

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series. PMID:29668743

On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs

NASA Astrophysics Data System (ADS)

Jiang, Minghui

We show that for any constant t ≥ 2, K -Independent Set and K-Dominating Set in t-track interval graphs are W[1]-hard. This settles an open question recently raised by Fellows, Hermelin, Rosamond, and Vialette. We also give an FPT algorithm for K-Clique in t-interval graphs, parameterized by both k and t, with running time max { t O(k), 2 O(klogk) } ·poly(n), where n is the number of vertices in the graph. This slightly improves the previous FPT algorithm by Fellows, Hermelin, Rosamond, and Vialette. Finally, we use the W[1]-hardness of K-Independent Set in t-track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called Maximal Strip Recovery (MSR). We show that MSR-d is W[1]-hard for any constant d ≥ 4 when the parameter is either the total length of the strips, or the total number of adjacencies in the strips, or the number of strips in the optimal solution.

A graph-based network-vulnerability analysis system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swiler, L.P.; Phillips, C.; Gaylor, T.

1998-05-03

This paper presents a graph based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example themore » class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level of effort for the attacker, various graph algorithms such as shortest path algorithms can identify the attack paths with the highest probability of success.« less

A graph-based network-vulnerability analysis system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swiler, L.P.; Phillips, C.; Gaylor, T.

1998-01-01

This report presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the classmore » of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.« less

A Set of Handwriting Features for Use in Automated Writer Identification.

PubMed

Miller, John J; Patterson, Robert Bradley; Gantz, Donald T; Saunders, Christopher P; Walch, Mark A; Buscaglia, JoAnn

2017-05-01

A writer's biometric identity can be characterized through the distribution of physical feature measurements ("writer's profile"); a graph-based system that facilitates the quantification of these features is described. To accomplish this quantification, handwriting is segmented into basic graphical forms ("graphemes"), which are "skeletonized" to yield the graphical topology of the handwritten segment. The graph-based matching algorithm compares the graphemes first by their graphical topology and then by their geometric features. Graphs derived from known writers can be compared against graphs extracted from unknown writings. The process is computationally intensive and relies heavily upon statistical pattern recognition algorithms. This article focuses on the quantification of these physical features and the construction of the associated pattern recognition methods for using the features to discriminate among writers. The graph-based system described in this article has been implemented in a highly accurate and approximately language-independent biometric recognition system of writers of cursive documents. © 2017 American Academy of Forensic Sciences.

Multi-View Multi-Instance Learning Based on Joint Sparse Representation and Multi-View Dictionary Learning.

PubMed

Li, Bing; Yuan, Chunfeng; Xiong, Weihua; Hu, Weiming; Peng, Houwen; Ding, Xinmiao; Maybank, Steve

2017-12-01

In multi-instance learning (MIL), the relations among instances in a bag convey important contextual information in many applications. Previous studies on MIL either ignore such relations or simply model them with a fixed graph structure so that the overall performance inevitably degrades in complex environments. To address this problem, this paper proposes a novel multi-view multi-instance learning algorithm (MIL) that combines multiple context structures in a bag into a unified framework. The novel aspects are: (i) we propose a sparse -graph model that can generate different graphs with different parameters to represent various context relations in a bag, (ii) we propose a multi-view joint sparse representation that integrates these graphs into a unified framework for bag classification, and (iii) we propose a multi-view dictionary learning algorithm to obtain a multi-view graph dictionary that considers cues from all views simultaneously to improve the discrimination of the MIL. Experiments and analyses in many practical applications prove the effectiveness of the M IL.

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression.

PubMed

Fasmer, Erlend Eindride; Fasmer, Ole Bernt; Berle, Jan Øystein; Oedegaard, Ketil J; Hauge, Erik R

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series.

Empirical Determination of Pattern Match Confidence in Labeled Graphs

DTIC Science & Technology

2014-02-07

were explored; Erdős–Rényi [6] random graphs, Barabási–Albert preferential attachment graphs [2], and Watts– Strogatz [18] small world graphs. The ER...B. Erdos - Renyi Barabasi - Albert Gr ap h Ty pe Strogatz - Watts Direct Within 2 nodes Within 4 nodes Search Limit 1 10 100 1000 10000 100000 100...Barabási–Albert (BA, crosses) and Watts– Strogatz (WS, trian- gles) graphs were generated with sizes ranging from 50 to 2500 nodes, and labeled

A learning approach to the bandwidth multicolouring problem

NASA Astrophysics Data System (ADS)

Akbari Torkestani, Javad

2016-05-01

In this article, a generalisation of the vertex colouring problem known as bandwidth multicolouring problem (BMCP), in which a set of colours is assigned to each vertex such that the difference between the colours, assigned to each vertex and its neighbours, is by no means less than a predefined threshold, is considered. It is shown that the proposed method can be applied to solve the bandwidth colouring problem (BCP) as well. BMCP is known to be NP-hard in graph theory, and so a large number of approximation solutions, as well as exact algorithms, have been proposed to solve it. In this article, two learning automata-based approximation algorithms are proposed for estimating a near-optimal solution to the BMCP. We show, for the first proposed algorithm, that by choosing a proper learning rate, the algorithm finds the optimal solution with a probability close enough to unity. Moreover, we compute the worst-case time complexity of the first algorithm for finding a 1/(1-ɛ) optimal solution to the given problem. The main advantage of this method is that a trade-off between the running time of algorithm and the colour set size (colouring optimality) can be made, by a proper choice of the learning rate also. Finally, it is shown that the running time of the proposed algorithm is independent of the graph size, and so it is a scalable algorithm for large graphs. The second proposed algorithm is compared with some well-known colouring algorithms and the results show the efficiency of the proposed algorithm in terms of the colour set size and running time of algorithm.

Dynamic graph of an oxy-fuel combustion system using autocatalytic set model

NASA Astrophysics Data System (ADS)

Harish, Noor Ainy; Bakar, Sumarni Abu

2017-08-01

Evaporation process is one of the main processes besides combustion process in an oxy-combustion boiler system. An Autocatalytic Set (ASC) Model has successfully applied in developing graphical representation of the chemical reactions that occurs in the evaporation process in the system. Seventeen variables identified in the process are represented as nodes and the catalytic relationships are represented as edges in the graph. In addition, in this paper graph dynamics of ACS is further investigated. By using Dynamic Autocatalytic Set Graph Algorithm (DAGA), the adjacency matrix for each of the graphs and its relations to Perron-Frobenius Theorem is investigated. The dynamic graph obtained is further investigated where the connection of the graph to fuzzy graph Type 1 is established.

Manipulating Google's Knowledge Graph Box to Counter Biased Information Processing During an Online Search on Vaccination: Application of a Technological Debiasing Strategy.

PubMed

Ludolph, Ramona; Allam, Ahmed; Schulz, Peter J

2016-06-02

One of people's major motives for going online is the search for health-related information. Most consumers start their search with a general search engine but are unaware of the fact that its sorting and ranking criteria do not mirror information quality. This misconception can lead to distorted search outcomes, especially when the information processing is characterized by heuristic principles and resulting cognitive biases instead of a systematic elaboration. As vaccination opponents are vocal on the Web, the chance of encountering their non‒evidence-based views on immunization is high. Therefore, biased information processing in this context can cause subsequent impaired judgment and decision making. A technological debiasing strategy could counter this by changing people's search environment. This study aims at testing a technological debiasing strategy to reduce the negative effects of biased information processing when using a general search engine on people's vaccination-related knowledge and attitudes. This strategy is to manipulate the content of Google's knowledge graph box, which is integrated in the search interface and provides basic information about the search topic. A full 3x2 factorial, posttest-only design was employed with availability of basic factual information (comprehensible vs hardly comprehensible vs not present) as the first factor and a warning message as the second factor of experimental manipulation. Outcome variables were the evaluation of the knowledge graph box, vaccination-related knowledge, as well as beliefs and attitudes toward vaccination, as represented by three latent variables emerged from an exploratory factor analysis. Two-way analysis of variance revealed a significant main effect of availability of basic information in the knowledge graph box on participants' vaccination knowledge scores (F2,273=4.86, P=.01), skepticism/fear of vaccination side effects (F2,273=3.5, P=.03), and perceived information quality (F2,273=3.73, P=.02). More specifically, respondents receiving comprehensible information appeared to be more knowledgeable, less skeptical of vaccination, and more critical of information quality compared to participants exposed to hardly comprehensible information. Although, there was no significant interaction effect between the availability of information and the presence of the warning, there was a dominant pattern in which the presence of the warning appeared to have a positive influence on the group receiving comprehensible information while the opposite was true for the groups exposed to hardly comprehensible information and no information at all. Participants evaluated the knowledge graph box as moderately to highly useful, with no significant differences among the experimental groups. Overall, the results suggest that comprehensible information in the knowledge graph box positively affects participants' vaccination-related knowledge and attitudes. A small change in the content retrieval procedure currently used by Google could already make a valuable difference in the pursuit of an unbiased online information search. Further research is needed to gain insights into the knowledge graph box's entire potential.

Optimal graph search segmentation using arc-weighted graph for simultaneous surface detection of bladder and prostate.

PubMed

Song, Qi; Wu, Xiaodong; Liu, Yunlong; Smith, Mark; Buatti, John; Sonka, Milan

2009-01-01

We present a novel method for globally optimal surface segmentation of multiple mutually interacting objects, incorporating both edge and shape knowledge in a 3-D graph-theoretic approach. Hard surface interacting constraints are enforced in the interacting regions, preserving the geometric relationship of those partially interacting surfaces. The soft smoothness a priori shape compliance is introduced into the energy functional to provide shape guidance. The globally optimal surfaces can be simultaneously achieved by solving a maximum flow problem based on an arc-weighted graph representation. Representing the segmentation problem in an arc-weighted graph, one can incorporate a wider spectrum of constraints into the formulation, thus increasing segmentation accuracy and robustness in volumetric image data. To the best of our knowledge, our method is the first attempt to introduce the arc-weighted graph representation into the graph-searching approach for simultaneous segmentation of multiple partially interacting objects, which admits a globally optimal solution in a low-order polynomial time. Our new approach was applied to the simultaneous surface detection of bladder and prostate. The result was quite encouraging in spite of the low saliency of the bladder and prostate in CT images.

Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images.

PubMed

Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

2017-02-01

Given the prevalence of joint photographic experts group (JPEG) compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform (DCT) coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors-Laplacian prior for DCT coefficients, sparsity prior, and graph-signal smoothness prior for image patches-to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the overcomplete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared with the previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms the state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

A Constant-Factor Approximation Algorithm for the Link Building Problem

NASA Astrophysics Data System (ADS)

Olsen, Martin; Viglas, Anastasios; Zvedeniouk, Ilia

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP. We present a polynomial time algorithm yielding a PageRank value within a constant factor from the optimal. We also consider the naive algorithm where we choose backlinks from nodes with high PageRank values compared to the outdegree and show that the naive algorithm performs much worse on certain graphs compared to the constant factor approximation scheme.

Local Higher-Order Graph Clustering

PubMed Central

Yin, Hao; Benson, Austin R.; Leskovec, Jure; Gleich, David F.

2018-01-01

Local graph clustering methods aim to find a cluster of nodes by exploring a small region of the graph. These methods are attractive because they enable targeted clustering around a given seed node and are faster than traditional global graph clustering methods because their runtime does not depend on the size of the input graph. However, current local graph partitioning methods are not designed to account for the higher-order structures crucial to the network, nor can they effectively handle directed networks. Here we introduce a new class of local graph clustering methods that address these issues by incorporating higher-order network information captured by small subgraphs, also called network motifs. We develop the Motif-based Approximate Personalized PageRank (MAPPR) algorithm that finds clusters containing a seed node with minimal motif conductance, a generalization of the conductance metric for network motifs. We generalize existing theory to prove the fast running time (independent of the size of the graph) and obtain theoretical guarantees on the cluster quality (in terms of motif conductance). We also develop a theory of node neighborhoods for finding sets that have small motif conductance, and apply these results to the case of finding good seed nodes to use as input to the MAPPR algorithm. Experimental validation on community detection tasks in both synthetic and real-world networks, shows that our new framework MAPPR outperforms the current edge-based personalized PageRank methodology. PMID:29770258

Graph Structure in Three National Academic Webs: Power Laws with Anomalies.

ERIC Educational Resources Information Center

Thelwall, Mike; Wilkinson, David

2003-01-01

Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)

Decentralized Control of Scheduling in Distributed Systems.

DTIC Science & Technology

1983-03-18

the job scheduling algorithm adapts to the changing busyness of the various hosts in the system. The environment in which the job scheduling entities...resources and processes that constitute the node and a set of interfaces for accessing these processes and resources. The structure of a node could change ...parallel. Chang [CHNG82] has also described some algorithms for detecting properties of general graphs by traversing paths in a graph in parallel. One of

Graph Based Models for Unsupervised High Dimensional Data Clustering and Network Analysis

DTIC Science & Technology

2015-01-01

ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for...algorithms we proposed improve the time e ciency signi cantly for large scale datasets. In the last chapter, we also propose an incremental reseeding...plume detection in hyper-spectral video data. These graph based clustering algorithms we proposed improve the time efficiency significantly for large

Salient object detection: manifold-based similarity adaptation approach

NASA Astrophysics Data System (ADS)

Zhou, Jingbo; Ren, Yongfeng; Yan, Yunyang; Gao, Shangbing

2014-11-01

A saliency detection algorithm based on manifold-based similarity adaptation is proposed. The proposed algorithm is divided into three steps. First, we segment an input image into superpixels, which are represented as the nodes in a graph. Second, a new similarity measurement is used in the proposed algorithm. The weight matrix of the graph, which indicates the similarities between the nodes, uses a similarity-based method. It also captures the manifold structure of the image patches, in which the graph edges are determined in a data adaptive manner in terms of both similarity and manifold structure. Then, we use local reconstruction method as a diffusion method to obtain the saliency maps. The objective function in the proposed method is based on local reconstruction, with which estimated weights capture the manifold structure. Experiments on four bench-mark databases demonstrate the accuracy and robustness of the proposed method.

Graph Kernels for Molecular Similarity.

PubMed

Rupp, Matthias; Schneider, Gisbert

2010-04-12

Molecular similarity measures are important for many cheminformatics applications like ligand-based virtual screening and quantitative structure-property relationships. Graph kernels are formal similarity measures defined directly on graphs, such as the (annotated) molecular structure graph. Graph kernels are positive semi-definite functions, i.e., they correspond to inner products. This property makes them suitable for use with kernel-based machine learning algorithms such as support vector machines and Gaussian processes. We review the major types of kernels between graphs (based on random walks, subgraphs, and optimal assignments, respectively), and discuss their advantages, limitations, and successful applications in cheminformatics. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fully Decomposable Split Graphs

NASA Astrophysics Data System (ADS)

Broersma, Hajo; Kratsch, Dieter; Woeginger, Gerhard J.

We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, i.e., whether it can be partitioned into connected parts of order α 1,α 2,...,α k for every α 1,α 2,...,α k summing up to the order of the graph. In contrast, we show that the decision problem whether a given split graph can be partitioned into connected parts of order α 1,α 2,...,α k for a given partition α 1,α 2,...,α k of the order of the graph, is NP-hard.

A Constraint-Based Planner for Data Production

NASA Technical Reports Server (NTRS)

Pang, Wanlin; Golden, Keith

2005-01-01

This paper presents a graph-based backtracking algorithm designed to support constrain-tbased planning in data production domains. This algorithm performs backtracking at two nested levels: the outer- backtracking following the structure of the planning graph to select planner subgoals and actions to achieve them and the inner-backtracking inside a subproblem associated with a selected action to find action parameter values. We show this algorithm works well in a planner applied to automating data production in an ecological forecasting system. We also discuss how the idea of multi-level backtracking may improve efficiency of solving semi-structured constraint problems.

Ring-like reliable PON planning with physical constraints for a smart grid

NASA Astrophysics Data System (ADS)

Wang, Xin; Gu, Rentao; Ji, Yuefeng

2016-01-01

Due to the high reliability requirements in the communication networks of a smart grid, a ring-like reliable PON is an ideal choice to carry power distribution information. Economical network planning is also very important for the smart grid communication infrastructure. Although the ring-like reliable PON has been widely used in the real applications, as far as we know, little research has been done on the network optimization subject of the ring-like reliable PON. Most PON planning research studies only consider a star-like topology or cascaded PON network, which barely guarantees the reliability requirements of the smart grid. In this paper, we mainly investigate the economical network planning problem for the ring-like reliable PON of the smart grid. To address this issue, we built a mathematical model for the planning problem of the ring-like reliable PON, and the objective was to minimize the total deployment costs under physical constraints. The model is simplified such that all of the nodes have the same properties, except OLT, because each potential splitter site can be located in the same ONU position in power communication networks. The simplified model is used to construct an optimal main tree topology in the complete graph and a backup-protected tree topology in the residual graph. An efficient heuristic algorithm, called the Constraints and Minimal Weight Oriented Fast Searching Algorithm (CMW-FSA), is proposed. In CMW-FSA, a feasible solution can be obtained directly with oriented constraints and a few recursive search processes. From the simulation results, the proposed planning model and CMW-FSA are verified to be accurate (the error rates are less than 0.4%) and effective compared with the accurate solution (CAESA), especially in small and sparse scenarios. The CMW-FSA significantly reduces the computation time compared with the CAESA. The time complexity algorithm of the CMW-FSA is acceptable and calculated as T(n) = O(n3). After evaluating the effects of the parameters of the two PON systems, the total planning costs of each scenario show a general declining trend and reach a threshold as the respective maximal transmission distances and maximal time delays increase.

Facilitating the 3D Indoor Search and Rescue Problem: An Overview of the Problem and an Ant Colony Solution Approach

NASA Astrophysics Data System (ADS)

Tashakkori, H.; Rajabifard, A.; Kalantari, M.

2016-10-01

Search and rescue procedures for indoor environments are quite complicated due to the fact that much of the indoor information is unavailable to rescuers before physical entrance to the incident scene. Thus, decision making regarding the number of crew required and the way they should be dispatched in the building considering the various access points and complexities in the buildings in order to cover the search area in minimum time is dependent on prior knowledge and experience of the emergency commanders. Hence, this paper introduces the Search and Rescue Problem (SRP) which aims at finding best search and rescue routes that minimize the overall search time in the buildings. 3D BIM-oriented indoor GIS is integrated in the indoor route graph to find accurate routes based on the building geometric and semantic information. An Ant Colony Based Algorithm is presented that finds the number of first responders required and their individual routes to search all rooms and points of interest inside the building to minimize the overall time spent by all rescuers inside the disaster area. The evaluation of the proposed model for a case study building shows a significant improve in search and rescue time which will lead to a higher chance of saving lives and less exposure of emergency crew to danger.

Accurate HLA type inference using a weighted similarity graph.

PubMed

Xie, Minzhu; Li, Jing; Jiang, Tao

2010-12-14

The human leukocyte antigen system (HLA) contains many highly variable genes. HLA genes play an important role in the human immune system, and HLA gene matching is crucial for the success of human organ transplantations. Numerous studies have demonstrated that variation in HLA genes is associated with many autoimmune, inflammatory and infectious diseases. However, typing HLA genes by serology or PCR is time consuming and expensive, which limits large-scale studies involving HLA genes. Since it is much easier and cheaper to obtain single nucleotide polymorphism (SNP) genotype data, accurate computational algorithms to infer HLA gene types from SNP genotype data are in need. To infer HLA types from SNP genotypes, the first step is to infer SNP haplotypes from genotypes. However, for the same SNP genotype data set, the haplotype configurations inferred by different methods are usually inconsistent, and it is often difficult to decide which one is true. In this paper, we design an accurate HLA gene type inference algorithm by utilizing SNP genotype data from pedigrees, known HLA gene types of some individuals and the relationship between inferred SNP haplotypes and HLA gene types. Given a set of haplotypes inferred from the genotypes of a population consisting of many pedigrees, the algorithm first constructs a weighted similarity graph based on a new haplotype similarity measure and derives constraint edges from known HLA gene types. Based on the principle that different HLA gene alleles should have different background haplotypes, the algorithm searches for an optimal labeling of all the haplotypes with unknown HLA gene types such that the total weight among the same HLA gene types is maximized. To deal with ambiguous haplotype solutions, we use a genetic algorithm to select haplotype configurations that tend to maximize the same optimization criterion. Our experiments on a previously typed subset of the HapMap data show that the algorithm is highly accurate, achieving an accuracy of 96% for gene HLA-A, 95% for HLA-B, 97% for HLA-C, 84% for HLA-DRB1, 98% for HLA-DQA1 and 97% for HLA-DQB1 in a leave-one-out test. Our algorithm can infer HLA gene types from neighboring SNP genotype data accurately. Compared with a recent approach on the same input data, our algorithm achieved a higher accuracy. The code of our algorithm is available to the public for free upon request to the corresponding authors.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services.

PubMed

Shi, Longxiang; Li, Shijian; Yang, Xiaoran; Qi, Jiaheng; Pan, Gang; Zhou, Binbin

2017-01-01

With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK), which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective.

Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services

PubMed Central

Yang, Xiaoran; Qi, Jiaheng; Pan, Gang; Zhou, Binbin

2017-01-01

With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK), which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective. PMID:28299322

Using Betweenness Centrality to Identify Manifold Shortcuts

PubMed Central

Cukierski, William J.; Foran, David J.

2010-01-01

High-dimensional data presents a challenge to tasks of pattern recognition and machine learning. Dimensionality reduction (DR) methods remove the unwanted variance and make these tasks tractable. Several nonlinear DR methods, such as the well known ISOMAP algorithm, rely on a neighborhood graph to compute geodesic distances between data points. These graphs can contain unwanted edges which connect disparate regions of one or more manifolds. This topological sensitivity is well known [1], [2], [3], yet handling high-dimensional, noisy data in the absence of a priori manifold knowledge, remains an open and difficult problem. This work introduces a divisive, edge-removal method based on graph betweenness centrality which can robustly identify manifold-shorting edges. The problem of graph construction in high dimension is discussed and the proposed algorithm is fit into the ISOMAP workflow. ROC analysis is performed and the performance is tested on synthetic and real datasets. PMID:20607142

GrouseFlocks: steerable exploration of graph hierarchy space.

PubMed

Archambault, Daniel; Munzner, Tamara; Auber, David

2008-01-01

Several previous systems allow users to interactively explore a large input graph through cuts of a superimposed hierarchy. This hierarchy is often created using clustering algorithms or topological features present in the graph. However, many graphs have domain-specific attributes associated with the nodes and edges, which could be used to create many possible hierarchies providing unique views of the input graph. GrouseFlocks is a system for the exploration of this graph hierarchy space. By allowing users to see several different possible hierarchies on the same graph, the system helps users investigate graph hierarchy space instead of a single fixed hierarchy. GrouseFlocks provides a simple set of operations so that users can create and modify their graph hierarchies based on selections. These selections can be made manually or based on patterns in the attribute data provided with the graph. It provides feedback to the user within seconds, allowing interactive exploration of this space.

Learning In networks

NASA Technical Reports Server (NTRS)

Buntine, Wray L.

1995-01-01

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deterministic nodes. Chain graphs are defined as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs are introduced to model independent samples. The paper concludes by discussing various operations that can be performed on chain graphs with plates as a simplification process or to generate learning algorithms.

PuReD-MCL: a graph-based PubMed document clustering methodology.

PubMed

Theodosiou, T; Darzentas, N; Angelis, L; Ouzounis, C A

2008-09-01

Biomedical literature is the principal repository of biomedical knowledge, with PubMed being the most complete database collecting, organizing and analyzing such textual knowledge. There are numerous efforts that attempt to exploit this information by using text mining and machine learning techniques. We developed a novel approach, called PuReD-MCL (Pubmed Related Documents-MCL), which is based on the graph clustering algorithm MCL and relevant resources from PubMed. PuReD-MCL avoids using natural language processing (NLP) techniques directly; instead, it takes advantage of existing resources, available from PubMed. PuReD-MCL then clusters documents efficiently using the MCL graph clustering algorithm, which is based on graph flow simulation. This process allows users to analyse the results by highlighting important clues, and finally to visualize the clusters and all relevant information using an interactive graph layout algorithm, for instance BioLayout Express 3D. The methodology was applied to two different datasets, previously used for the validation of the document clustering tool TextQuest. The first dataset involves the organisms Escherichia coli and yeast, whereas the second is related to Drosophila development. PuReD-MCL successfully reproduces the annotated results obtained from TextQuest, while at the same time provides additional insights into the clusters and the corresponding documents. Source code in perl and R are available from http://tartara.csd.auth.gr/~theodos/

Solving traveling salesman problems with DNA molecules encoding numerical values.

PubMed

Lee, Ji Youn; Shin, Soo-Yong; Park, Tai Hyun; Zhang, Byoung-Tak

2004-12-01

We introduce a DNA encoding method to represent numerical values and a biased molecular algorithm based on the thermodynamic properties of DNA. DNA strands are designed to encode real values by variation of their melting temperatures. The thermodynamic properties of DNA are used for effective local search of optimal solutions using biochemical techniques, such as denaturation temperature gradient polymerase chain reaction and temperature gradient gel electrophoresis. The proposed method was successfully applied to the traveling salesman problem, an instance of optimization problems on weighted graphs. This work extends the capability of DNA computing to solving numerical optimization problems, which is contrasted with other DNA computing methods focusing on logical problem solving.

Graph traversals, genes, and matroids: An efficient case of the travelling salesman problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gusfield, D.; Stelling, P.; Wang, Lusheng

1996-12-31

In this paper the authors consider graph traversal problems that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). They first explain the connection of the graph problems to SBH and then focus on the traversal problems. They describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide a bounded-error approximation algorithm for the maximum weight TSP in a superset of those directed graphs. The authors also establish the existence of a matroid structure defined on the set ofmore » Euler and Hamilton paths in the restricted class of graphs. 8 refs., 5 figs.« less

Automatic segmentation of the choroid in enhanced depth imaging optical coherence tomography images.

PubMed

Tian, Jing; Marziliano, Pina; Baskaran, Mani; Tun, Tin Aung; Aung, Tin

2013-03-01

Enhanced Depth Imaging (EDI) optical coherence tomography (OCT) provides high-definition cross-sectional images of the choroid in vivo, and hence is used in many clinical studies. However, the quantification of the choroid depends on the manual labelings of two boundaries, Bruch's membrane and the choroidal-scleral interface. This labeling process is tedious and subjective of inter-observer differences, hence, automatic segmentation of the choroid layer is highly desirable. In this paper, we present a fast and accurate algorithm that could segment the choroid automatically. Bruch's membrane is detected by searching the pixel with the biggest gradient value above the retinal pigment epithelium (RPE) and the choroidal-scleral interface is delineated by finding the shortest path of the graph formed by valley pixels using Dijkstra's algorithm. The experiments comparing automatic segmentation results with the manual labelings are conducted on 45 EDI-OCT images and the average of Dice's Coefficient is 90.5%, which shows good consistency of the algorithm with the manual labelings. The processing time for each image is about 1.25 seconds.

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

2018-01-01

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

Nonschematic drawing recognition: a new approach based on attributed graph grammar with flexible embedding

NASA Astrophysics Data System (ADS)

Lee, Kyu J.; Kunii, T. L.; Noma, T.

1993-01-01

In this paper, we propose a syntactic pattern recognition method for non-schematic drawings, based on a new attributed graph grammar with flexible embedding. In our graph grammar, the embedding rule permits the nodes of a guest graph to be arbitrarily connected with the nodes of a host graph. The ambiguity caused by this flexible embedding is controlled with the evaluation of synthesized attributes and the check of context sensitivity. To integrate parsing with the synthesized attribute evaluation and the context sensitivity check, we also develop a bottom up parsing algorithm.

JavaGenes and Condor: Cycle-Scavenging Genetic Algorithms

NASA Technical Reports Server (NTRS)

Globus, Al; Langhirt, Eric; Livny, Miron; Ramamurthy, Ravishankar; Soloman, Marvin; Traugott, Steve

2000-01-01

A genetic algorithm code, JavaGenes, was written in Java and used to evolve pharmaceutical drug molecules and digital circuits. JavaGenes was run under the Condor cycle-scavenging batch system managing 100-170 desktop SGI workstations. Genetic algorithms mimic biological evolution by evolving solutions to problems using crossover and mutation. While most genetic algorithms evolve strings or trees, JavaGenes evolves graphs representing (currently) molecules and circuits. Java was chosen as the implementation language because the genetic algorithm requires random splitting and recombining of graphs, a complex data structure manipulation with ample opportunities for memory leaks, loose pointers, out-of-bound indices, and other hard to find bugs. Java garbage-collection memory management, lack of pointer arithmetic, and array-bounds index checking prevents these bugs from occurring, substantially reducing development time. While a run-time performance penalty must be paid, the only unacceptable performance we encountered was using standard Java serialization to checkpoint and restart the code. This was fixed by a two-day implementation of custom checkpointing. JavaGenes is minimally integrated with Condor; in other words, JavaGenes must do its own checkpointing and I/O redirection. A prototype Java-aware version of Condor was developed using standard Java serialization for checkpointing. For the prototype to be useful, standard Java serialization must be significantly optimized. JavaGenes is approximately 8700 lines of code and a few thousand JavaGenes jobs have been run. Most jobs ran for a few days. Results include proof that genetic algorithms can evolve directed and undirected graphs, development of a novel crossover operator for graphs, a paper in the journal Nanotechnology, and another paper in preparation.

Predicting overlapping protein complexes from weighted protein interaction graphs by gradually expanding dense neighborhoods.

PubMed

Dimitrakopoulos, Christos; Theofilatos, Konstantinos; Pegkas, Andreas; Likothanassis, Spiros; Mavroudi, Seferina

2016-07-01

Proteins are vital biological molecules driving many fundamental cellular processes. They rarely act alone, but form interacting groups called protein complexes. The study of protein complexes is a key goal in systems biology. Recently, large protein-protein interaction (PPI) datasets have been published and a plethora of computational methods that provide new ideas for the prediction of protein complexes have been implemented. However, most of the methods suffer from two major limitations: First, they do not account for proteins participating in multiple functions and second, they are unable to handle weighted PPI graphs. Moreover, the problem remains open as existing algorithms and tools are insufficient in terms of predictive metrics. In the present paper, we propose gradually expanding neighborhoods with adjustment (GENA), a new algorithm that gradually expands neighborhoods in a graph starting from highly informative "seed" nodes. GENA considers proteins as multifunctional molecules allowing them to participate in more than one protein complex. In addition, GENA accepts weighted PPI graphs by using a weighted evaluation function for each cluster. In experiments with datasets from Saccharomyces cerevisiae and human, GENA outperformed Markov clustering, restricted neighborhood search and clustering with overlapping neighborhood expansion, three state-of-the-art methods for computationally predicting protein complexes. Seven PPI networks and seven evaluation datasets were used in total. GENA outperformed existing methods in 16 out of 18 experiments achieving an average improvement of 5.5% when the maximum matching ratio metric was used. Our method was able to discover functionally homogeneous protein clusters and uncover important network modules in a Parkinson expression dataset. When used on the human networks, around 47% of the detected clusters were enriched in gene ontology (GO) terms with depth higher than five in the GO hierarchy. In the present manuscript, we introduce a new method for the computational prediction of protein complexes by making the realistic assumption that proteins participate in multiple protein complexes and cellular functions. Our method can detect accurate and functionally homogeneous clusters. Copyright © 2016 Elsevier B.V. All rights reserved.

Multi-target Detection, Tracking, and Data Association on Road Networks Using Unmanned Aerial Vehicles

NASA Astrophysics Data System (ADS)

Barkley, Brett E.

A cooperative detection and tracking algorithm for multiple targets constrained to a road network is presented for fixed-wing Unmanned Air Vehicles (UAVs) with a finite field of view. Road networks of interest are formed into graphs with nodes that indicate the target likelihood ratio (before detection) and position probability (after detection). A Bayesian likelihood ratio tracker recursively assimilates target observations until the cumulative observations at a particular location pass a detection criterion. At this point, a target is considered detected and a position probability is generated for the target on the graph. Data association is subsequently used to route future measurements to update the likelihood ratio tracker (for undetected target) or to update a position probability (a previously detected target). Three strategies for motion planning of UAVs are proposed to balance searching for new targets with tracking known targets for a variety of scenarios. Performance was tested in Monte Carlo simulations for a variety of mission parameters, including tracking on road networks with varying complexity and using UAVs at various altitudes.

A greedy, graph-based algorithm for the alignment of multiple homologous gene lists.

PubMed

Fostier, Jan; Proost, Sebastian; Dhoedt, Bart; Saeys, Yvan; Demeester, Piet; Van de Peer, Yves; Vandepoele, Klaas

2011-03-15

Many comparative genomics studies rely on the correct identification of homologous genomic regions using accurate alignment tools. In such case, the alphabet of the input sequences consists of complete genes, rather than nucleotides or amino acids. As optimal multiple sequence alignment is computationally impractical, a progressive alignment strategy is often employed. However, such an approach is susceptible to the propagation of alignment errors in early pairwise alignment steps, especially when dealing with strongly diverged genomic regions. In this article, we present a novel accurate and efficient greedy, graph-based algorithm for the alignment of multiple homologous genomic segments, represented as ordered gene lists. Based on provable properties of the graph structure, several heuristics are developed to resolve local alignment conflicts that occur due to gene duplication and/or rearrangement events on the different genomic segments. The performance of the algorithm is assessed by comparing the alignment results of homologous genomic segments in Arabidopsis thaliana to those obtained by using both a progressive alignment method and an earlier graph-based implementation. Especially for datasets that contain strongly diverged segments, the proposed method achieves a substantially higher alignment accuracy, and proves to be sufficiently fast for large datasets including a few dozens of eukaryotic genomes. http://bioinformatics.psb.ugent.be/software. The algorithm is implemented as a part of the i-ADHoRe 3.0 package.

RGB-D SLAM Combining Visual Odometry and Extended Information Filter

PubMed Central

Zhang, Heng; Liu, Yanli; Tan, Jindong; Xiong, Naixue

2015-01-01

In this paper, we present a novel RGB-D SLAM system based on visual odometry and an extended information filter, which does not require any other sensors or odometry. In contrast to the graph optimization approaches, this is more suitable for online applications. A visual dead reckoning algorithm based on visual residuals is devised, which is used to estimate motion control input. In addition, we use a novel descriptor called binary robust appearance and normals descriptor (BRAND) to extract features from the RGB-D frame and use them as landmarks. Furthermore, considering both the 3D positions and the BRAND descriptors of the landmarks, our observation model avoids explicit data association between the observations and the map by marginalizing the observation likelihood over all possible associations. Experimental validation is provided, which compares the proposed RGB-D SLAM algorithm with just RGB-D visual odometry and a graph-based RGB-D SLAM algorithm using the publicly-available RGB-D dataset. The results of the experiments demonstrate that our system is quicker than the graph-based RGB-D SLAM algorithm. PMID:26263990

Differentially Private Frequent Subgraph Mining

PubMed Central

Xu, Shengzhi; Xiong, Li; Cheng, Xiang; Xiao, Ke

2016-01-01

Mining frequent subgraphs from a collection of input graphs is an important topic in data mining research. However, if the input graphs contain sensitive information, releasing frequent subgraphs may pose considerable threats to individual's privacy. In this paper, we study the problem of frequent subgraph mining (FGM) under the rigorous differential privacy model. We introduce a novel differentially private FGM algorithm, which is referred to as DFG. In this algorithm, we first privately identify frequent subgraphs from input graphs, and then compute the noisy support of each identified frequent subgraph. In particular, to privately identify frequent subgraphs, we present a frequent subgraph identification approach which can improve the utility of frequent subgraph identifications through candidates pruning. Moreover, to compute the noisy support of each identified frequent subgraph, we devise a lattice-based noisy support derivation approach, where a series of methods has been proposed to improve the accuracy of the noisy supports. Through formal privacy analysis, we prove that our DFG algorithm satisfies ε-differential privacy. Extensive experimental results on real datasets show that the DFG algorithm can privately find frequent subgraphs with high data utility. PMID:27616876

Enumerating Substituted Benzene Isomers of Tree-Like Chemical Graphs.

PubMed

Li, Jinghui; Nagamochi, Hiroshi; Akutsu, Tatsuya

2018-01-01

Enumeration of chemical structures is useful for drug design, which is one of the main targets of computational biology and bioinformatics. A chemical graph with no other cycles than benzene rings is called tree-like, and becomes a tree possibly with multiple edges if we contract each benzene ring into a single virtual atom of valence 6. All tree-like chemical graphs with a given tree representation are called the substituted benzene isomers of . When we replace each virtual atom in with a benzene ring to obtain a substituted benzene isomer, distinct isomers of are caused by the difference in arrangements of atom groups around a benzene ring. In this paper, we propose an efficient algorithm that enumerates all substituted benzene isomers of a given tree representation . Our algorithm first counts the number of all the isomers of the tree representation by a dynamic programming method. To enumerate all the isomers, for each , our algorithm then generates the th isomer by backtracking the counting phase of the dynamic programming. We also implemented our algorithm for computational experiments.

Comparison and Evaluation of Clustering Algorithms for Tandem Mass Spectra.

PubMed

Rieder, Vera; Schork, Karin U; Kerschke, Laura; Blank-Landeshammer, Bernhard; Sickmann, Albert; Rahnenführer, Jörg

2017-11-03

In proteomics, liquid chromatography-tandem mass spectrometry (LC-MS/MS) is established for identifying peptides and proteins. Duplicated spectra, that is, multiple spectra of the same peptide, occur both in single MS/MS runs and in large spectral libraries. Clustering tandem mass spectra is used to find consensus spectra, with manifold applications. First, it speeds up database searches, as performed for instance by Mascot. Second, it helps to identify novel peptides across species. Third, it is used for quality control to detect wrongly annotated spectra. We compare different clustering algorithms based on the cosine distance between spectra. CAST, MS-Cluster, and PRIDE Cluster are popular algorithms to cluster tandem mass spectra. We add well-known algorithms for large data sets, hierarchical clustering, DBSCAN, and connected components of a graph, as well as the new method N-Cluster. All algorithms are evaluated on real data with varied parameter settings. Cluster results are compared with each other and with peptide annotations based on validation measures such as purity. Quality control, regarding the detection of wrongly (un)annotated spectra, is discussed for exemplary resulting clusters. N-Cluster proves to be highly competitive. All clustering results benefit from the so-called DISMS2 filter that integrates additional information, for example, on precursor mass.

Hierarchical graphs for rule-based modeling of biochemical systems

PubMed Central

2011-01-01

Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models. PMID:21288338

Application of the PageRank Algorithm to Alarm Graphs

NASA Astrophysics Data System (ADS)

Treinen, James J.; Thurimella, Ramakrishna

The task of separating genuine attacks from false alarms in large intrusion detection infrastructures is extremely difficult. The number of alarms received in such environments can easily enter into the millions of alerts per day. The overwhelming noise created by these alarms can cause genuine attacks to go unnoticed. As means of highlighting these attacks, we introduce a host ranking technique utilizing Alarm Graphs. Rather than enumerate all potential attack paths as in Attack Graphs, we build and analyze graphs based on the alarms generated by the intrusion detection sensors installed on a network. Given that the alarms are predominantly false positives, the challenge is to identify, separate, and ideally predict future attacks. In this paper, we propose a novel approach to tackle this problem based on the PageRank algorithm. By elevating the rank of known attackers and victims we are able to observe the effect that these hosts have on the other nodes in the Alarm Graph. Using this information we are able to discover previously overlooked attacks, as well as defend against future intrusions.

Manipulating Google’s Knowledge Graph Box to Counter Biased Information Processing During an Online Search on Vaccination: Application of a Technological Debiasing Strategy

PubMed Central

Allam, Ahmed; Schulz, Peter J

2016-01-01

Background One of people’s major motives for going online is the search for health-related information. Most consumers start their search with a general search engine but are unaware of the fact that its sorting and ranking criteria do not mirror information quality. This misconception can lead to distorted search outcomes, especially when the information processing is characterized by heuristic principles and resulting cognitive biases instead of a systematic elaboration. As vaccination opponents are vocal on the Web, the chance of encountering their non‒evidence-based views on immunization is high. Therefore, biased information processing in this context can cause subsequent impaired judgment and decision making. A technological debiasing strategy could counter this by changing people’s search environment. Objective This study aims at testing a technological debiasing strategy to reduce the negative effects of biased information processing when using a general search engine on people’s vaccination-related knowledge and attitudes. This strategy is to manipulate the content of Google’s knowledge graph box, which is integrated in the search interface and provides basic information about the search topic. Methods A full 3x2 factorial, posttest-only design was employed with availability of basic factual information (comprehensible vs hardly comprehensible vs not present) as the first factor and a warning message as the second factor of experimental manipulation. Outcome variables were the evaluation of the knowledge graph box, vaccination-related knowledge, as well as beliefs and attitudes toward vaccination, as represented by three latent variables emerged from an exploratory factor analysis. Results Two-way analysis of variance revealed a significant main effect of availability of basic information in the knowledge graph box on participants’ vaccination knowledge scores (F2,273=4.86, P=.01), skepticism/fear of vaccination side effects (F2,273=3.5, P=.03), and perceived information quality (F2,273=3.73, P=.02). More specifically, respondents receiving comprehensible information appeared to be more knowledgeable, less skeptical of vaccination, and more critical of information quality compared to participants exposed to hardly comprehensible information. Although, there was no significant interaction effect between the availability of information and the presence of the warning, there was a dominant pattern in which the presence of the warning appeared to have a positive influence on the group receiving comprehensible information while the opposite was true for the groups exposed to hardly comprehensible information and no information at all. Participants evaluated the knowledge graph box as moderately to highly useful, with no significant differences among the experimental groups. Conclusion Overall, the results suggest that comprehensible information in the knowledge graph box positively affects participants’ vaccination-related knowledge and attitudes. A small change in the content retrieval procedure currently used by Google could already make a valuable difference in the pursuit of an unbiased online information search. Further research is needed to gain insights into the knowledge graph box’s entire potential. PMID:27255736

Efficient Algorithmic Frameworks via Structural Graph Theory

DTIC Science & Technology

2016-10-28

centrally planned solution. Policy recommendation: Given a socioeconomic game among multiple parties (countries, armies, political parties, terrorist...etc.). 2 Graph Structure of Network Creation Games We completed the final versions of two of our papers about the graph structure inherent in...network creation games ”, which appeared in the following venues: Erik D. Demaine, MohammadTaghi Hajiaghayi, Hamid Mahini, and Morteza Zadi- moghaddam, “The

Mining relational paths in integrated biomedical data.

PubMed

He, Bing; Tang, Jie; Ding, Ying; Wang, Huijun; Sun, Yuyin; Shin, Jae Hong; Chen, Bin; Moorthy, Ganesh; Qiu, Judy; Desai, Pankaj; Wild, David J

2011-01-01

Much life science and biology research requires an understanding of complex relationships between biological entities (genes, compounds, pathways, diseases, and so on). There is a wealth of data on such relationships in publicly available datasets and publications, but these sources are overlapped and distributed so that finding pertinent relational data is increasingly difficult. Whilst most public datasets have associated tools for searching, there is a lack of searching methods that can cross data sources and that in particular search not only based on the biological entities themselves but also on the relationships between them. In this paper, we demonstrate how graph-theoretic algorithms for mining relational paths can be used together with a previous integrative data resource we developed called Chem2Bio2RDF to extract new biological insights about the relationships between such entities. In particular, we use these methods to investigate the genetic basis of side-effects of thiazolinedione drugs, and in particular make a hypothesis for the recently discovered cardiac side-effects of Rosiglitazone (Avandia) and a prediction for Pioglitazone which is backed up by recent clinical studies.

GRADIENT: Graph Analytic Approach for Discovering Irregular Events, Nascent and Temporal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogan, Emilie

2015-03-31

Finding a time-ordered signature within large graphs is a computationally complex problem due to the combinatorial explosion of potential patterns. GRADIENT is designed to search and understand that problem space.

GRADIENT: Graph Analytic Approach for Discovering Irregular Events, Nascent and Temporal

ScienceCinema

Hogan, Emilie

2018-01-16

Finding a time-ordered signature within large graphs is a computationally complex problem due to the combinatorial explosion of potential patterns. GRADIENT is designed to search and understand that problem space.

Rapid Onboard Trajectory Design for Autonomous Spacecraft in Multibody Systems

NASA Astrophysics Data System (ADS)

Trumbauer, Eric Michael

This research develops automated, on-board trajectory planning algorithms in order to support current and new mission concepts. These include orbiter missions to Phobos or Deimos, Outer Planet Moon orbiters, and robotic and crewed missions to small bodies. The challenges stem from the limited on-board computing resources which restrict full trajectory optimization with guaranteed convergence in complex dynamical environments. The approach taken consists of leveraging pre-mission computations to create a large database of pre-computed orbits and arcs. Such a database is used to generate a discrete representation of the dynamics in the form of a directed graph, which acts to index these arcs. This allows the use of graph search algorithms on-board in order to provide good approximate solutions to the path planning problem. Coupled with robust differential correction and optimization techniques, this enables the determination of an efficient path between any boundary conditions with very little time and computing effort. Furthermore, the optimization methods developed here based on sequential convex programming are shown to have provable convergence properties, as well as generating feasible major iterates in case of a system interrupt -- a key requirement for on-board application. The outcome of this project is thus the development of an algorithmic framework which allows the deployment of this approach in a variety of specific mission contexts. Test cases related to missions of interest to NASA and JPL such as a Phobos orbiter and a Near Earth Asteroid interceptor are demonstrated, including the results of an implementation on the RAD750 flight processor. This method fills a gap in the toolbox being developed to create fully autonomous space exploration systems.

A Weight-Adaptive Laplacian Embedding for Graph-Based Clustering.

PubMed

Cheng, De; Nie, Feiping; Sun, Jiande; Gong, Yihong

2017-07-01

Graph-based clustering methods perform clustering on a fixed input data graph. Thus such clustering results are sensitive to the particular graph construction. If this initial construction is of low quality, the resulting clustering may also be of low quality. We address this drawback by allowing the data graph itself to be adaptively adjusted in the clustering procedure. In particular, our proposed weight adaptive Laplacian (WAL) method learns a new data similarity matrix that can adaptively adjust the initial graph according to the similarity weight in the input data graph. We develop three versions of these methods based on the L2-norm, fuzzy entropy regularizer, and another exponential-based weight strategy, that yield three new graph-based clustering objectives. We derive optimization algorithms to solve these objectives. Experimental results on synthetic data sets and real-world benchmark data sets exhibit the effectiveness of these new graph-based clustering methods.

Neurally and Ocularly Informed Graph-Based Models for Searching 3D Environments

DTIC Science & Technology

2014-06-03

hBCI = hybrid brain–computer interface, TAG = transductive annotation by graph, CV = computer vision, TSP = traveling salesman problem . are navigated...environment that are most likely to contain objects that the subject would like to visit. 2.9. Route planning A traveling salesman problem (TSP) solver...fixations in a visual search task using fixation-related potentials J. Vis. 13 Croes G 1958 A method for solving traveling - salesman problems Oper. Res

Heuristic-driven graph wavelet modeling of complex terrain

NASA Astrophysics Data System (ADS)

Cioacǎ, Teodor; Dumitrescu, Bogdan; Stupariu, Mihai-Sorin; Pǎtru-Stupariu, Ileana; Nǎpǎrus, Magdalena; Stoicescu, Ioana; Peringer, Alexander; Buttler, Alexandre; Golay, François

2015-03-01

We present a novel method for building a multi-resolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the lazy wavelet node partitioning, we employ an attribute aware cost function based on the generalized quadric error metric. The resulting algorithm can be applied to multivariate data by storing additional attributes at the graph's nodes. We discuss how the cost computation mechanism can be coupled with the lifting scheme and examine the results by evaluating the root mean square error. The algorithm is experimentally tested using two multivariate LiDAR sets representing terrain surface and vegetation structure with different sampling densities.

Identifying Vulnerabilities and Hardening Attack Graphs for Networked Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saha, Sudip; Vullinati, Anil K.; Halappanavar, Mahantesh

We investigate efficient security control methods for protecting against vulnerabilities in networked systems. A large number of interdependent vulnerabilities typically exist in the computing nodes of a cyber-system; as vulnerabilities get exploited, starting from low level ones, they open up the doors to more critical vulnerabilities. These cannot be understood just by a topological analysis of the network, and we use the attack graph abstraction of Dewri et al. to study these problems. In contrast to earlier approaches based on heuristics and evolutionary algorithms, we study rigorous methods for quantifying the inherent vulnerability and hardening cost for the system. Wemore » develop algorithms with provable approximation guarantees, and evaluate them for real and synthetic attack graphs.« less

Figure-ground segmentation based on class-independent shape priors

NASA Astrophysics Data System (ADS)

Li, Yang; Liu, Yang; Liu, Guojun; Guo, Maozu

2018-01-01

We propose a method to generate figure-ground segmentation by incorporating shape priors into the graph-cuts algorithm. Given an image, we first obtain a linear representation of an image and then apply directional chamfer matching to generate class-independent, nonparametric shape priors, which provide shape clues for the graph-cuts algorithm. We then enforce shape priors in a graph-cuts energy function to produce object segmentation. In contrast to previous segmentation methods, the proposed method shares shape knowledge for different semantic classes and does not require class-specific model training. Therefore, the approach obtains high-quality segmentation for objects. We experimentally validate that the proposed method outperforms previous approaches using the challenging PASCAL VOC 2010/2012 and Berkeley (BSD300) segmentation datasets.

A graph-based approach to construct target-focused libraries for virtual screening.

PubMed

Naderi, Misagh; Alvin, Chris; Ding, Yun; Mukhopadhyay, Supratik; Brylinski, Michal

2016-01-01

Due to exorbitant costs of high-throughput screening, many drug discovery projects commonly employ inexpensive virtual screening to support experimental efforts. However, the vast majority of compounds in widely used screening libraries, such as the ZINC database, will have a very low probability to exhibit the desired bioactivity for a given protein. Although combinatorial chemistry methods can be used to augment existing compound libraries with novel drug-like compounds, the broad chemical space is often too large to be explored. Consequently, the trend in library design has shifted to produce screening collections specifically tailored to modulate the function of a particular target or a protein family. Assuming that organic compounds are composed of sets of rigid fragments connected by flexible linkers, a molecule can be decomposed into its building blocks tracking their atomic connectivity. On this account, we developed eSynth, an exhaustive graph-based search algorithm to computationally synthesize new compounds by reconnecting these building blocks following their connectivity patterns. We conducted a series of benchmarking calculations against the Directory of Useful Decoys, Enhanced database. First, in a self-benchmarking test, the correctness of the algorithm is validated with the objective to recover a molecule from its building blocks. Encouragingly, eSynth can efficiently rebuild more than 80 % of active molecules from their fragment components. Next, the capability to discover novel scaffolds is assessed in a cross-benchmarking test, where eSynth successfully reconstructed 40 % of the target molecules using fragments extracted from chemically distinct compounds. Despite an enormous chemical space to be explored, eSynth is computationally efficient; half of the molecules are rebuilt in less than a second, whereas 90 % take only about a minute to be generated. eSynth can successfully reconstruct chemically feasible molecules from molecular fragments. Furthermore, in a procedure mimicking the real application, where one expects to discover novel compounds based on a small set of already developed bioactives, eSynth is capable of generating diverse collections of molecules with the desired activity profiles. Thus, we are very optimistic that our effort will contribute to targeted drug discovery. eSynth is freely available to the academic community at www.brylinski.org/content/molecular-synthesis.Graphical abstractAssuming that organic compounds are composed of sets of rigid fragments connected by flexible linkers, a molecule can be decomposed into its building blocks tracking their atomic connectivity. Here, we developed eSynth, an automated method to synthesize new compounds by reconnecting these building blocks following the connectivity patterns via an exhaustive graph-based search algorithm. eSynth opens up a possibility to rapidly construct virtual screening libraries for targeted drug discovery.

Analysis of Community Detection Algorithms for Large Scale Cyber Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mane, Prachita; Shanbhag, Sunanda; Kamath, Tanmayee

The aim of this project is to use existing community detection algorithms on an IP network dataset to create supernodes within the network. This study compares the performance of different algorithms on the network in terms of running time. The paper begins with an introduction to the concept of clustering and community detection followed by the research question that the team aimed to address. Further the paper describes the graph metrics that were considered in order to shortlist algorithms followed by a brief explanation of each algorithm with respect to the graph metric on which it is based. The nextmore » section in the paper describes the methodology used by the team in order to run the algorithms and determine which algorithm is most efficient with respect to running time. Finally, the last section of the paper includes the results obtained by the team and a conclusion based on those results as well as future work.« less

A graph-based system for network-vulnerability analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swiler, L.P.; Phillips, C.

1998-06-01

This paper presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The graph-based tool can identify the set of attack paths that have a high probability of success (or a low effort cost) for the attacker. The system could be used to test the effectiveness of making configuration changes, implementing an intrusion detection system, etc. The analysis system requires as input a database of common attacks,more » broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.« less

TreeNetViz: revealing patterns of networks over tree structures.

PubMed

Gou, Liang; Zhang, Xiaolong Luke

2011-12-01

Network data often contain important attributes from various dimensions such as social affiliations and areas of expertise in a social network. If such attributes exhibit a tree structure, visualizing a compound graph consisting of tree and network structures becomes complicated. How to visually reveal patterns of a network over a tree has not been fully studied. In this paper, we propose a compound graph model, TreeNet, to support visualization and analysis of a network at multiple levels of aggregation over a tree. We also present a visualization design, TreeNetViz, to offer the multiscale and cross-scale exploration and interaction of a TreeNet graph. TreeNetViz uses a Radial, Space-Filling (RSF) visualization to represent the tree structure, a circle layout with novel optimization to show aggregated networks derived from TreeNet, and an edge bundling technique to reduce visual complexity. Our circular layout algorithm reduces both total edge-crossings and edge length and also considers hierarchical structure constraints and edge weight in a TreeNet graph. These experiments illustrate that the algorithm can reduce visual cluttering in TreeNet graphs. Our case study also shows that TreeNetViz has the potential to support the analysis of a compound graph by revealing multiscale and cross-scale network patterns. © 2011 IEEE

Graphical Representations of Electronic Search Patterns.

ERIC Educational Resources Information Center

Lin, Xia; And Others

1991-01-01

Discussion of search behavior in electronic environments focuses on the development of GRIP (Graphic Representor of Interaction Patterns), a graphing tool based on HyperCard that produces graphic representations of search patterns. Search state spaces are explained, and forms of data available from electronic searches are described. (34…

GreedyMAX-type Algorithms for the Maximum Independent Set Problem

NASA Astrophysics Data System (ADS)

Borowiecki, Piotr; Göring, Frank

A maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued function p defined on the vertex set V(G) and called a potential function of a graph G, while P(G) = max v ∈ V(G) p(v) is called a potential of G. For any graph P(G) ≤ Δ(G), where Δ(G) is the maximum degree of G. Moreover, Δ(G) - P(G) may be arbitrarily large. A potential of a vertex lets us get a closer insight into the properties of its neighborhood which leads to the definition of the family of GreedyMAX-type algorithms having the classical GreedyMAX algorithm as their origin. We establish a lower bound 1/(P + 1) for the performance ratio of GreedyMAX-type algorithms which favorably compares with the bound 1/(Δ + 1) known to hold for GreedyMAX. The cardinality of an independent set generated by any GreedyMAX-type algorithm is at least sum_{vin V(G)} (p(v)+1)^{-1}, which strengthens the bounds of Turán and Caro-Wei stated in terms of vertex degrees.

Reaction factoring and bipartite update graphs accelerate the Gillespie Algorithm for large-scale biochemical systems.

PubMed

Indurkhya, Sagar; Beal, Jacob

2010-01-06

ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models.

Reaction Factoring and Bipartite Update Graphs Accelerate the Gillespie Algorithm for Large-Scale Biochemical Systems

PubMed Central

Indurkhya, Sagar; Beal, Jacob

2010-01-01

ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models. PMID:20066048

A hierarchical graph neuron scheme for real-time pattern recognition.

PubMed

Nasution, B B; Khan, A I

2008-02-01

The hierarchical graph neuron (HGN) implements a single cycle memorization and recall operation through a novel algorithmic design. The HGN is an improvement on the already published original graph neuron (GN) algorithm. In this improved approach, it recognizes incomplete/noisy patterns. It also resolves the crosstalk problem, which is identified in the previous publications, within closely matched patterns. To accomplish this, the HGN links multiple GN networks for filtering noise and crosstalk out of pattern data inputs. Intrinsically, the HGN is a lightweight in-network processing algorithm which does not require expensive floating point computations; hence, it is very suitable for real-time applications and tiny devices such as the wireless sensor networks. This paper describes that the HGN's pattern matching capability and the small response time remain insensitive to the increases in the number of stored patterns. Moreover, the HGN does not require definition of rules or setting of thresholds by the operator to achieve the desired results nor does it require heuristics entailing iterative operations for memorization and recall of patterns.

Visibility graphs and symbolic dynamics

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Just, Wolfram

2018-07-01

Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology nontrivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the time series. Hence, Pesin's identity suggests that these block entropies are converging to the Kolmogorov-Sinai entropy of the physical measure, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x) , x ∈ [ 0 , 1 ] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs.

A Clustering Graph Generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey

In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps tomore » understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.« less

An Expert System toward Buiding An Earth Science Knowledge Graph

NASA Astrophysics Data System (ADS)

Zhang, J.; Duan, X.; Ramachandran, R.; Lee, T. J.; Bao, Q.; Gatlin, P. N.; Maskey, M.

2017-12-01

In this ongoing work, we aim to build foundations of Cognitive Computing for Earth Science research. The goal of our project is to develop an end-to-end automated methodology for incrementally constructing Knowledge Graphs for Earth Science (KG4ES). These knowledge graphs can then serve as the foundational components for building cognitive systems in Earth science, enabling researchers to uncover new patterns and hypotheses that are virtually impossible to identify today. In addition, this research focuses on developing mining algorithms needed to exploit these constructed knowledge graphs. As such, these graphs will free knowledge from publications that are generated in a very linear, deterministic manner, and structure knowledge in a way that users can both interact and connect with relevant pieces of information. Our major contributions are two-fold. First, we have developed an end-to-end methodology for constructing Knowledge Graphs for Earth Science (KG4ES) using existing corpus of journal papers and reports. One of the key challenges in any machine learning, especially deep learning applications, is the need for robust and large training datasets. We have developed techniques capable of automatically retraining models and incrementally building and updating KG4ES, based on ever evolving training data. We also adopt the evaluation instrument based on common research methodologies used in Earth science research, especially in Atmospheric Science. Second, we have developed an algorithm to infer new knowledge that can exploit the constructed KG4ES. In more detail, we have developed a network prediction algorithm aiming to explore and predict possible new connections in the KG4ES and aid in new knowledge discovery.

LSG: An External-Memory Tool to Compute String Graphs for Next-Generation Sequencing Data Assembly.

PubMed

Bonizzoni, Paola; Vedova, Gianluca Della; Pirola, Yuri; Previtali, Marco; Rizzi, Raffaella

2016-03-01

The large amount of short read data that has to be assembled in future applications, such as in metagenomics or cancer genomics, strongly motivates the investigation of disk-based approaches to index next-generation sequencing (NGS) data. Positive results in this direction stimulate the investigation of efficient external memory algorithms for de novo assembly from NGS data. Our article is also motivated by the open problem of designing a space-efficient algorithm to compute a string graph using an indexing procedure based on the Burrows-Wheeler transform (BWT). We have developed a disk-based algorithm for computing string graphs in external memory: the light string graph (LSG). LSG relies on a new representation of the FM-index that is exploited to use an amount of main memory requirement that is independent from the size of the data set. Moreover, we have developed a pipeline for genome assembly from NGS data that integrates LSG with the assembly step of SGA (Simpson and Durbin, 2012 ), a state-of-the-art string graph-based assembler, and uses BEETL for indexing the input data. LSG is open source software and is available online. We have analyzed our implementation on a 875-million read whole-genome dataset, on which LSG has built the string graph using only 1GB of main memory (reducing the memory occupation by a factor of 50 with respect to SGA), while requiring slightly more than twice the time than SGA. The analysis of the entire pipeline shows an important decrease in memory usage, while managing to have only a moderate increase in the running time.

Graph processing platforms at scale: practices and experiences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Seung-Hwan; Lee, Sangkeun; Brown, Tyler C

2015-01-01

Graph analysis unveils hidden associations of data in many phenomena and artifacts, such as road network, social networks, genomic information, and scientific collaboration. Unfortunately, a wide diversity in the characteristics of graphs and graph operations make it challenging to find a right combination of tools and implementation of algorithms to discover desired knowledge from the target data set. This study presents an extensive empirical study of three representative graph processing platforms: Pegasus, GraphX, and Urika. Each system represents a combination of options in data model, processing paradigm, and infrastructure. We benchmarked each platform using three popular graph operations, degree distribution,more » connected components, and PageRank over a variety of real-world graphs. Our experiments show that each graph processing platform shows different strength, depending the type of graph operations. While Urika performs the best in non-iterative operations like degree distribution, GraphX outputforms iterative operations like connected components and PageRank. In addition, we discuss challenges to optimize the performance of each platform over large scale real world graphs.« less

Normalized Cut Algorithm for Automated Assignment of Protein Domains

NASA Technical Reports Server (NTRS)

Samanta, M. P.; Liang, S.; Zha, H.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

We present a novel computational method for automatic assignment of protein domains from structural data. At the core of our algorithm lies a recently proposed clustering technique that has been very successful for image-partitioning applications. This grap.,l-theory based clustering method uses the notion of a normalized cut to partition. an undirected graph into its strongly-connected components. Computer implementation of our method tested on the standard comparison set of proteins from the literature shows a high success rate (84%), better than most existing alternative In addition, several other features of our algorithm, such as reliance on few adjustable parameters, linear run-time with respect to the size of the protein and reduced complexity compared to other graph-theory based algorithms, would make it an attractive tool for structural biologists.