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.

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

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

Enhancing PC Cluster-Based Parallel Branch-and-Bound Algorithms for the Graph Coloring Problem

NASA Astrophysics Data System (ADS)

Taoka, Satoshi; Takafuji, Daisuke; Watanabe, Toshimasa

A branch-and-bound algorithm (BB for short) is the most general technique to deal with various combinatorial optimization problems. Even if it is used, computation time is likely to increase exponentially. So we consider its parallelization to reduce it. It has been reported that the computation time of a parallel BB heavily depends upon node-variable selection strategies. And, in case of a parallel BB, it is also necessary to prevent increase in communication time. So, it is important to pay attention to how many and what kind of nodes are to be transferred (called sending-node selection strategy). In this paper, for the graph coloring problem, we propose some sending-node selection strategies for a parallel BB algorithm by adopting MPI for parallelization and experimentally evaluate how these strategies affect computation time of a parallel BB on a PC cluster network.

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

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

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.

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

Highly Asynchronous VisitOr Queue Graph Toolkit

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

Pearce, R.

2012-10-01

HAVOQGT is a C++ framework that can be used to create highly parallel graph traversal algorithms. The framework stores the graph and algorithmic data structures on external memory that is typically mapped to high performance locally attached NAND FLASH arrays. The framework supports a vertex-centered visitor programming model. The frameworkd has been used to implement breadth first search, connected components, and single source shortest path.

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.

A parallel computing engine for a class of time critical processes.

PubMed

Nabhan, T M; Zomaya, A Y

1997-01-01

This paper focuses on the efficient parallel implementation of systems of numerically intensive nature over loosely coupled multiprocessor architectures. These analytical models are of significant importance to many real-time systems that have to meet severe time constants. A parallel computing engine (PCE) has been developed in this work for the efficient simplification and the near optimal scheduling of numerical models over the different cooperating processors of the parallel computer. First, the analytical system is efficiently coded in its general form. The model is then simplified by using any available information (e.g., constant parameters). A task graph representing the interconnections among the different components (or equations) is generated. The graph can then be compressed to control the computation/communication requirements. The task scheduler employs a graph-based iterative scheme, based on the simulated annealing algorithm, to map the vertices of the task graph onto a Multiple-Instruction-stream Multiple-Data-stream (MIMD) type of architecture. The algorithm uses a nonanalytical cost function that properly considers the computation capability of the processors, the network topology, the communication time, and congestion possibilities. Moreover, the proposed technique is simple, flexible, and computationally viable. The efficiency of the algorithm is demonstrated by two case studies with good results.

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

Scalable Static and Dynamic Community Detection Using Grappolo

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

Halappanavar, Mahantesh; Lu, Hao; Kalyanaraman, Anantharaman

Graph clustering, popularly known as community detection, is a fundamental kernel for several applications of relevance to the Defense Advanced Research Projects Agency’s (DARPA) Hierarchical Identify Verify Exploit (HIVE) Pro- gram. Clusters or communities represent natural divisions within a network that are densely connected within a cluster and sparsely connected to the rest of the network. The need to compute clustering on large scale data necessitates the development of efficient algorithms that can exploit modern architectures that are fundamentally parallel in nature. How- ever, due to their irregular and inherently sequential nature, many of the current algorithms for community detectionmore » are challenging to parallelize. In response to the HIVE Graph Challenge, we present several parallelization heuristics for fast community detection using the Louvain method as the serial template. We implement all the heuristics in a software library called Grappolo. Using the inputs from the HIVE Challenge, we demonstrate superior performance and high quality solutions based on four parallelization heuristics. We use Grappolo on static graphs as the first step towards community detection on streaming graphs.« less

Plane representations of graphs and visibility between parallel segments

NASA Astrophysics Data System (ADS)

Tamassia, R.; Tollis, I. G.

1985-04-01

Several layout compaction strategies for VLSI are based on the concept of visibility between parallel segments, where we say that two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment. This paper studies visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments drawn between visible vertex-segments. Clearly, every graph that admits such a representation must be a planar. The authors consider three types of visibility representations, and give complete characterizations of the classes of graphs that admit them. Furthermore, they present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs.

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

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.

A new scheduling algorithm for parallel sparse LU factorization with static pivoting

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

Grigori, Laura; Li, Xiaoye S.

2002-08-20

In this paper we present a static scheduling algorithm for parallel sparse LU factorization with static pivoting. The algorithm is divided into mapping and scheduling phases, using the symmetric pruned graphs of L' and U to represent dependencies. The scheduling algorithm is designed for driving the parallel execution of the factorization on a distributed-memory architecture. Experimental results and comparisons with SuperLU{_}DIST are reported after applying this algorithm on real world application matrices on an IBM SP RS/6000 distributed memory machine.

Array distribution in data-parallel programs

NASA Technical Reports Server (NTRS)

Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert; Sheffler, Thomas J.

1994-01-01

We consider distribution at compile time of the array data in a distributed-memory implementation of a data-parallel program written in a language like Fortran 90. We allow dynamic redistribution of data and define a heuristic algorithmic framework that chooses distribution parameters to minimize an estimate of program completion time. We represent the program as an alignment-distribution graph. We propose a divide-and-conquer algorithm for distribution that initially assigns a common distribution to each node of the graph and successively refines this assignment, taking computation, realignment, and redistribution costs into account. We explain how to estimate the effect of distribution on computation cost and how to choose a candidate set of distributions. We present the results of an implementation of our algorithms on several test problems.

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.

Scaling Semantic Graph Databases in Size and Performance

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

Morari, Alessandro; Castellana, Vito G.; Villa, Oreste

In this paper we present SGEM, a full software system for accelerating large-scale semantic graph databases on commodity clusters. Unlike current approaches, SGEM addresses semantic graph databases by only employing graph methods at all the levels of the stack. On one hand, this allows exploiting the space efficiency of graph data structures and the inherent parallelism of graph algorithms. These features adapt well to the increasing system memory and core counts of modern commodity clusters. On the other hand, however, these systems are optimized for regular computation and batched data transfers, while graph methods usually are irregular and generate fine-grainedmore » data accesses with poor spatial and temporal locality. Our framework comprises a SPARQL to data parallel C compiler, a library of parallel graph methods and a custom, multithreaded runtime system. We introduce our stack, motivate its advantages with respect to other solutions and show how we solved the challenges posed by irregular behaviors. We present the result of our software stack on the Berlin SPARQL benchmarks with datasets up to 10 billion triples (a triple corresponds to a graph edge), demonstrating scaling in dataset size and in performance as more nodes are added to the cluster.« less

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

Parallel approach for bioinspired algorithms

NASA Astrophysics Data System (ADS)

Zaporozhets, Dmitry; Zaruba, Daria; Kulieva, Nina

2018-05-01

In the paper, a probabilistic parallel approach based on the population heuristic, such as a genetic algorithm, is suggested. The authors proposed using a multithreading approach at the micro level at which new alternative solutions are generated. On each iteration, several threads that independently used the same population to generate new solutions can be started. After the work of all threads, a selection operator combines obtained results in the new population. To confirm the effectiveness of the suggested approach, the authors have developed software on the basis of which experimental computations can be carried out. The authors have considered a classic optimization problem – finding a Hamiltonian cycle in a graph. Experiments show that due to the parallel approach at the micro level, increment of running speed can be obtained on graphs with 250 and more vertices.

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

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.

XDATA

DTIC Science & Technology

2017-05-01

Parallelizing PINT The main focus of our research into the parallelization of the PINT algorithm has been to find appropriately scalable matrix math algorithms...leading eigenvector of the adjacency matrix of the pairwise affinity graph. We reviewed the matrix math implementation currently being used in PINT and...the new versions support a feature called matrix.distributed, which is some level of support for distributed matrix math ; however our code is not

The Complexity of Parallel Algorithms,

DTIC Science & Technology

1985-11-01

programns have been written for se(luiential coiipn ters. Many p~eop~le want coimp ~ilers dihal. will c(nimpile t he, code for parallel machines, to avoid...between two vertices. We also rely on parallel algorithms for maintaining data structures and manipulating graphs. We do not go into the details of these...Jpatlis and maintain connected coimp ~onents. The routine is: - 35 .- ExtendPath(r, Q, V) begin P +-0; s 4- while there is a path in V - P from s to a vertex

Scalable Parallel Density-based Clustering and Applications

NASA Astrophysics Data System (ADS)

Patwary, Mostofa Ali

2014-04-01

Recently, density-based clustering algorithms (DBSCAN and OPTICS) have gotten significant attention of the scientific community due to their unique capability of discovering arbitrary shaped clusters and eliminating noise data. These algorithms have several applications, which require high performance computing, including finding halos and subhalos (clusters) from massive cosmology data in astrophysics, analyzing satellite images, X-ray crystallography, and anomaly detection. However, parallelization of these algorithms are extremely challenging as they exhibit inherent sequential data access order, unbalanced workload resulting in low parallel efficiency. To break the data access sequentiality and to achieve high parallelism, we develop new parallel algorithms, both for DBSCAN and OPTICS, designed using graph algorithmic techniques. For example, our parallel DBSCAN algorithm exploits the similarities between DBSCAN and computing connected components. Using datasets containing up to a billion floating point numbers, we show that our parallel density-based clustering algorithms significantly outperform the existing algorithms, achieving speedups up to 27.5 on 40 cores on shared memory architecture and speedups up to 5,765 using 8,192 cores on distributed memory architecture. In our experiments, we found that while achieving the scalability, our algorithms produce clustering results with comparable quality to the classical algorithms.

A Hybrid Parallel Strategy Based on String Graph Theory to Improve De Novo DNA Assembly on the TianHe-2 Supercomputer.

PubMed

Zhang, Feng; Liao, Xiangke; Peng, Shaoliang; Cui, Yingbo; Wang, Bingqiang; Zhu, Xiaoqian; Liu, Jie

2016-06-01

' The de novo assembly of DNA sequences is increasingly important for biological researches in the genomic era. After more than one decade since the Human Genome Project, some challenges still exist and new solutions are being explored to improve de novo assembly of genomes. String graph assembler (SGA), based on the string graph theory, is a new method/tool developed to address the challenges. In this paper, based on an in-depth analysis of SGA we prove that the SGA-based sequence de novo assembly is an NP-complete problem. According to our analysis, SGA outperforms other similar methods/tools in memory consumption, but costs much more time, of which 60-70 % is spent on the index construction. Upon this analysis, we introduce a hybrid parallel optimization algorithm and implement this algorithm in the TianHe-2's parallel framework. Simulations are performed with different datasets. For data of small size the optimized solution is 3.06 times faster than before, and for data of middle size it's 1.60 times. The results demonstrate an evident performance improvement, with the linear scalability for parallel FM-index construction. This results thus contribute significantly to improving the efficiency of de novo assembly of DNA sequences.

Update on Development of Mesh Generation Algorithms in MeshKit

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

Jain, Rajeev; Vanderzee, Evan; Mahadevan, Vijay

2015-09-30

MeshKit uses a graph-based design for coding all its meshing algorithms, which includes the Reactor Geometry (and mesh) Generation (RGG) algorithms. This report highlights the developmental updates of all the algorithms, results and future work. Parallel versions of algorithms, documentation and performance results are reported. RGG GUI design was updated to incorporate new features requested by the users; boundary layer generation and parallel RGG support were added to the GUI. Key contributions to the release, upgrade and maintenance of other SIGMA1 libraries (CGM and MOAB) were made. Several fundamental meshing algorithms for creating a robust parallel meshing pipeline in MeshKitmore » are under development. Results and current status of automated, open-source and high quality nuclear reactor assembly mesh generation algorithms such as trimesher, quadmesher, interval matching and multi-sweeper are reported.« less

Matching Theory - A Sampler: From Denes Koenig to the Present

DTIC Science & Technology

1991-01-01

1079. [1131 , Matching Theory, Ann. Discrete Math . 29, North- Holland, Amsterdam, 1986. [114 ] M. Luby, A simple parallel algorithm for the maximal...311. [135 ]M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. [1361 , Matching extension and the genus of a graph, J. Combin...Theory Ser. B, 44, 1988, 329-837. [137] , A theorem on matchings in the plane, Graph Theory in Memory of G.A. Dirac, Ann. Discrete Math . 41, North

Optimizing Approximate Weighted Matching on Nvidia Kepler K40

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

Naim, Md; Manne, Fredrik; Halappanavar, Mahantesh

Matching is a fundamental graph problem with numerous applications in science and engineering. While algorithms for computing optimal matchings are difficult to parallelize, approximation algorithms on the other hand generally compute high quality solutions and are amenable to parallelization. In this paper, we present efficient implementations of the current best algorithm for half-approximate weighted matching, the Suitor algorithm, on Nvidia Kepler K-40 platform. We develop four variants of the algorithm that exploit hardware features to address key challenges for a GPU implementation. We also experiment with different combinations of work assigned to a warp. Using an exhaustive set ofmore » $269$ inputs, we demonstrate that the new implementation outperforms the previous best GPU algorithm by $10$ to $$100\\times$$ for over $100$ instances, and from $100$ to $$1000\\times$$ for $15$ instances. We also demonstrate up to $$20\\times$$ speedup relative to $2$ threads, and up to $$5\\times$$ relative to $16$ threads on Intel Xeon platform with $16$ cores for the same algorithm. The new algorithms and implementations provided in this paper will have a direct impact on several applications that repeatedly use matching as a key compute kernel. Further, algorithm designs and insights provided in this paper will benefit other researchers implementing graph algorithms on modern GPU architectures.« less

DNA Assembly with De Bruijn Graphs Using an FPGA Platform.

PubMed

Poirier, Carl; Gosselin, Benoit; Fortier, Paul

2018-01-01

This paper presents an FPGA implementation of a DNA assembly algorithm, called Ray, initially developed to run on parallel CPUs. The OpenCL language is used and the focus is placed on modifying and optimizing the original algorithm to better suit the new parallelization tool and the radically different hardware architecture. The results show that the execution time is roughly one fourth that of the CPU and factoring energy consumption yields a tenfold savings.

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.

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

Demeure, I.M.

The research presented here is concerned with representation techniques and tools to support the design, prototyping, simulation, and evaluation of message-based parallel, distributed computations. The author describes ParaDiGM-Parallel, Distributed computation Graph Model-a visual representation technique for parallel, message-based distributed computations. ParaDiGM provides several views of a computation depending on the aspect of concern. It is made of two complementary submodels, the DCPG-Distributed Computing Precedence Graph-model, and the PAM-Process Architecture Model-model. DCPGs are precedence graphs used to express the functionality of a computation in terms of tasks, message-passing, and data. PAM graphs are used to represent the partitioning of a computationmore » into schedulable units or processes, and the pattern of communication among those units. There is a natural mapping between the two models. He illustrates the utility of ParaDiGM as a representation technique by applying it to various computations (e.g., an adaptive global optimization algorithm, the client-server model). ParaDiGM representations are concise. They can be used in documenting the design and the implementation of parallel, distributed computations, in describing such computations to colleagues, and in comparing and contrasting various implementations of the same computation. He then describes VISA-VISual Assistant, a software tool to support the design, prototyping, and simulation of message-based parallel, distributed computations. VISA is based on the ParaDiGM model. In particular, it supports the editing of ParaDiGM graphs to describe the computations of interest, and the animation of these graphs to provide visual feedback during simulations. The graphs are supplemented with various attributes, simulation parameters, and interpretations which are procedures that can be executed by VISA.« less

Solving very large, sparse linear systems on mesh-connected parallel computers

NASA Technical Reports Server (NTRS)

Opsahl, Torstein; Reif, John

1987-01-01

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

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

A Faster Parallel Algorithm and Efficient Multithreaded Implementations for Evaluating Betweenness Centrality on Massive Datasets

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

Madduri, Kamesh; Ediger, David; Jiang, Karl

2009-05-29

We present a new lock-free parallel algorithm for computing betweenness centrality of massive small-world networks. With minor changes to the data structures, our algorithm also achieves better spatial cache locality compared to previous approaches. Betweenness centrality is a key algorithm kernel in the HPCS SSCA#2 Graph Analysis benchmark, which has been extensively used to evaluate the performance of emerging high-performance computing architectures for graph-theoretic computations. We design optimized implementations of betweenness centrality and the SSCA#2 benchmark for two hardware multithreaded systems: a Cray XMT system with the ThreadStorm processor, and a single-socket Sun multicore server with the UltraSparc T2 processor.more » For a small-world network of 134 million vertices and 1.073 billion edges, the 16-processor XMT system and the 8-core Sun Fire T5120 server achieve TEPS scores (an algorithmic performance count for the SSCA#2 benchmark) of 160 million and 90 million respectively, which corresponds to more than a 2X performance improvement over the previous parallel implementations. To better characterize the performance of these multithreaded systems, we correlate the SSCA#2 performance results with data from the memory-intensive STREAM and RandomAccess benchmarks. Finally, we demonstrate the applicability of our implementation to analyze massive real-world datasets by computing approximate betweenness centrality for a large-scale IMDb movie-actor network.« less

Design and Implementation of Parallel Algorithms

DTIC Science & Technology

1992-05-01

Alon, N., Y. Azar, and Y. Ravid [1990]. "Universal sequences for complete graphs," SIAM J. Discrete Math 27. Alon, N., A. Bar-Noy, N. Linial, and D...SIAM J. Discrete Math .’ Klein, P., S. A. Plotkin, C. Stein, and E. Tardos [19911. "Faster approximation algorithms for the unit capacity concurrent

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.

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

Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments

NASA Technical Reports Server (NTRS)

Bisws, Rupak; Kumar, Shailendra; Das, Sajal K.; Biegel, Bryan (Technical Monitor)

2002-01-01

The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.

A Hybrid Shared-Memory Parallel Max-Tree Algorithm for Extreme Dynamic-Range Images.

PubMed

Moschini, Ugo; Meijster, Arnold; Wilkinson, Michael H F

2018-03-01

Max-trees, or component trees, are graph structures that represent the connected components of an image in a hierarchical way. Nowadays, many application fields rely on images with high-dynamic range or floating point values. Efficient sequential algorithms exist to build trees and compute attributes for images of any bit depth. However, we show that the current parallel algorithms perform poorly already with integers at bit depths higher than 16 bits per pixel. We propose a parallel method combining the two worlds of flooding and merging max-tree algorithms. First, a pilot max-tree of a quantized version of the image is built in parallel using a flooding method. Later, this structure is used in a parallel leaf-to-root approach to compute efficiently the final max-tree and to drive the merging of the sub-trees computed by the threads. We present an analysis of the performance both on simulated and actual 2D images and 3D volumes. Execution times are about better than the fastest sequential algorithm and speed-up goes up to on 64 threads.

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.

Parallelizing flow-accumulation calculations on graphics processing units—From iterative DEM preprocessing algorithm to recursive multiple-flow-direction algorithm

NASA Astrophysics Data System (ADS)

Qin, Cheng-Zhi; Zhan, Lijun

2012-06-01

As one of the important tasks in digital terrain analysis, the calculation of flow accumulations from gridded digital elevation models (DEMs) usually involves two steps in a real application: (1) using an iterative DEM preprocessing algorithm to remove the depressions and flat areas commonly contained in real DEMs, and (2) using a recursive flow-direction algorithm to calculate the flow accumulation for every cell in the DEM. Because both algorithms are computationally intensive, quick calculation of the flow accumulations from a DEM (especially for a large area) presents a practical challenge to personal computer (PC) users. In recent years, rapid increases in hardware capacity of the graphics processing units (GPUs) provided in modern PCs have made it possible to meet this challenge in a PC environment. Parallel computing on GPUs using a compute-unified-device-architecture (CUDA) programming model has been explored to speed up the execution of the single-flow-direction algorithm (SFD). However, the parallel implementation on a GPU of the multiple-flow-direction (MFD) algorithm, which generally performs better than the SFD algorithm, has not been reported. Moreover, GPU-based parallelization of the DEM preprocessing step in the flow-accumulation calculations has not been addressed. This paper proposes a parallel approach to calculate flow accumulations (including both iterative DEM preprocessing and a recursive MFD algorithm) on a CUDA-compatible GPU. For the parallelization of an MFD algorithm (MFD-md), two different parallelization strategies using a GPU are explored. The first parallelization strategy, which has been used in the existing parallel SFD algorithm on GPU, has the problem of computing redundancy. Therefore, we designed a parallelization strategy based on graph theory. The application results show that the proposed parallel approach to calculate flow accumulations on a GPU performs much faster than either sequential algorithms or other parallel GPU-based algorithms based on existing parallelization strategies.

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.

Combinatorial structures to modeling simple games and applications

NASA Astrophysics Data System (ADS)

Molinero, Xavier

2017-09-01

We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.

Parametric binary dissection

NASA Technical Reports Server (NTRS)

Bokhari, Shahid H.; Crockett, Thomas W.; Nicol, David M.

1993-01-01

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.

Exact parallel algorithms for some members of the traveling salesman problem family

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

Pekny, J.F.

1989-01-01

The traveling salesman problem and its many generalizations comprise one of the best known combinatorial optimization problem families. Most members of the family are NP-complete problems so that exact algorithms require an unpredictable and sometimes large computational effort. Parallel computers offer hope for providing the power required to meet these demands. A major barrier to applying parallel computers is the lack of parallel algorithms. The contributions presented in this thesis center around new exact parallel algorithms for the asymmetric traveling salesman problem (ATSP), prize collecting traveling salesman problem (PCTSP), and resource constrained traveling salesman problem (RCTSP). The RCTSP is amore » particularly difficult member of the family since finding a feasible solution is an NP-complete problem. An exact sequential algorithm is also presented for the directed hamiltonian cycle problem (DHCP). The DHCP algorithm is superior to current heuristic approaches and represents the first exact method applicable to large graphs. Computational results presented for each of the algorithms demonstrates the effectiveness of combining efficient algorithms with parallel computing methods. Performance statistics are reported for randomly generated ATSPs with 7,500 cities, PCTSPs with 200 cities, RCTSPs with 200 cities, DHCPs with 3,500 vertices, and assignment problems of size 10,000. Sequential results were collected on a Sun 4/260 engineering workstation, while parallel results were collected using a 14 and 100 processor BBN Butterfly Plus computer. The computational results represent the largest instances ever solved to optimality on any type of computer.« less

On the relationship between parallel computation and graph embedding

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

Gupta, A.K.

1989-01-01

The problem of efficiently simulating an algorithm designed for an n-processor parallel machine G on an m-processor parallel machine H with n > m arises when parallel algorithms designed for an ideal size machine are simulated on existing machines which are of a fixed size. The author studies this problem when every processor of H takes over the function of a number of processors in G, and he phrases the simulation problem as a graph embedding problem. New embeddings presented address relevant issues arising from the parallel computation environment. The main focus centers around embedding complete binary trees into smaller-sizedmore » binary trees, butterflies, and hypercubes. He also considers simultaneous embeddings of r source machines into a single hypercube. Constant factors play a crucial role in his embeddings since they are not only important in practice but also lead to interesting theoretical problems. All of his embeddings minimize dilation and load, which are the conventional cost measures in graph embeddings and determine the maximum amount of time required to simulate one step of G on H. His embeddings also optimize a new cost measure called ({alpha},{beta})-utilization which characterizes how evenly the processors of H are used by the processors of G. Ideally, the utilization should be balanced (i.e., every processor of H simulates at most (n/m) processors of G) and the ({alpha},{beta})-utilization measures how far off from a balanced utilization the embedding is. He presents embeddings for the situation when some processors of G have different capabilities (e.g. memory or I/O) than others and the processors with different capabilities are to be distributed uniformly among the processors of H. Placing such conditions on an embedding results in an increase in some of the cost measures.« less

Parallel and Distributed Systems for Probabilistic Reasoning

DTIC Science & Technology

2012-12-01

work at CMU I had the opportunity to work with Andreas Krause on Gaussian process models for signal quality estimation in wireless sensor networks ...we reviewed the natural parallelization of the belief propagation algorithm using the synchronous schedule and demonstrated both theoretically and...problem is that the power-law sparsity structure, commonly found in graphs derived from natural phenomena (e.g., social networks and the web

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.

Hybrid Parallel Contour Trees, Version 1.0

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

Sewell, Christopher; Fasel, Patricia; Carr, Hamish

A common operation in scientific visualization is to compute and render a contour of a data set. Given a function of the form f : R^d -> R, a level set is defined as an inverse image f^-1(h) for an isovalue h, and a contour is a single connected component of a level set. The Reeb graph can then be defined to be the result of contracting each contour to a single point, and is well defined for Euclidean spaces or for general manifolds. For simple domains, the graph is guaranteed to be a tree, and is called the contourmore » tree. Analysis can then be performed on the contour tree in order to identify isovalues of particular interest, based on various metrics, and render the corresponding contours, without having to know such isovalues a priori. This code is intended to be the first data-parallel algorithm for computing contour trees. Our implementation will use the portable data-parallel primitives provided by Nvidia’s Thrust library, allowing us to compile our same code for both GPUs and multi-core CPUs. Native OpenMP and purely serial versions of the code will likely also be included. It will also be extended to provide a hybrid data-parallel / distributed algorithm, allowing scaling beyond a single GPU or CPU.« less

Optimal processor assignment for pipeline computations

NASA Technical Reports Server (NTRS)

Nicol, David M.; Simha, Rahul; Choudhury, Alok N.; Narahari, Bhagirath

1991-01-01

The availability of large scale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual responses times for different processor sizes, find an assignment of processor to tasks. Two objectives are of interest: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, it is assumed that a large number of processors are to be assigned to a relatively small number of tasks. Efficient assignment algorithms were developed for different classes of task structures. For a p processor system and a series parallel precedence graph with n constituent tasks, an O(np2) algorithm is provided that finds the optimal assignment for the response time optimization problem; it was found that the assignment optimizing the constrained throughput in O(np2log p) time. Special cases of linear, independent, and tree graphs are also considered.

Algorithms for Data Intensive Applications on Intelligent and Smart Memories

DTIC Science & Technology

2003-03-01

editors). Parallel Algorithms and Architectures. North Holland, 1986. [8] P. Diniz . USC ISI, Personal Communication, March, 2001. [9] M. Frigo, C. E ...hierarchy as well as the Translation Lookaside Buer TLB aect the e ectiveness of cache friendly optimizations These penalties vary among...processors and cause large variations in the e ectiveness of cache performance optimizations The area of graph problems is fundamental in a wide variety of

Efficient sequential and parallel algorithms for record linkage.

PubMed

Mamun, Abdullah-Al; Mi, Tian; Aseltine, Robert; Rajasekaran, Sanguthevar

2014-01-01

Integrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms. Our algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components. Our sequential and parallel algorithms have been tested on a real dataset of 1,083,878 records and synthetic datasets ranging in size from 50,000 to 9,000,000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes). We have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm.

Efficient parallel architecture for highly coupled real-time linear system applications

NASA Technical Reports Server (NTRS)

Carroll, Chester C.; Homaifar, Abdollah; Barua, Soumavo

1988-01-01

A systematic procedure is developed for exploiting the parallel constructs of computation in a highly coupled, linear system application. An overall top-down design approach is adopted. Differential equations governing the application under consideration are partitioned into subtasks on the basis of a data flow analysis. The interconnected task units constitute a task graph which has to be computed in every update interval. Multiprocessing concepts utilizing parallel integration algorithms are then applied for efficient task graph execution. A simple scheduling routine is developed to handle task allocation while in the multiprocessor mode. Results of simulation and scheduling are compared on the basis of standard performance indices. Processor timing diagrams are developed on the basis of program output accruing to an optimal set of processors. Basic architectural attributes for implementing the system are discussed together with suggestions for processing element design. Emphasis is placed on flexible architectures capable of accommodating widely varying application specifics.

Parallel processing optimization strategy based on MapReduce model in cloud storage environment

NASA Astrophysics Data System (ADS)

Cui, Jianming; Liu, Jiayi; Li, Qiuyan

2017-05-01

Currently, a large number of documents in the cloud storage process employed the way of packaging after receiving all the packets. From the local transmitter this stored procedure to the server, packing and unpacking will consume a lot of time, and the transmission efficiency is low as well. A new parallel processing algorithm is proposed to optimize the transmission mode. According to the operation machine graphs model work, using MPI technology parallel execution Mapper and Reducer mechanism. It is good to use MPI technology to implement Mapper and Reducer parallel mechanism. After the simulation experiment of Hadoop cloud computing platform, this algorithm can not only accelerate the file transfer rate, but also shorten the waiting time of the Reducer mechanism. It will break through traditional sequential transmission constraints and reduce the storage coupling to improve the transmission efficiency.

Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing

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

B. Hendrickson; T.G. Kolda

1998-09-01

A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

DOE PAGES

Azad, Ariful; Ballard, Grey; Buluc, Aydin; ...

2016-11-08

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achievingmore » significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.« less

Streaming data analytics via message passing with application to graph algorithms

DOE PAGES

Plimpton, Steven J.; Shead, Tim

2014-05-06

The need to process streaming data, which arrives continuously at high-volume in real-time, arises in a variety of contexts including data produced by experiments, collections of environmental or network sensors, and running simulations. Streaming data can also be formulated as queries or transactions which operate on a large dynamic data store, e.g. a distributed database. We describe a lightweight, portable framework named PHISH which enables a set of independent processes to compute on a stream of data in a distributed-memory parallel manner. Datums are routed between processes in patterns defined by the application. PHISH can run on top of eithermore » message-passing via MPI or sockets via ZMQ. The former means streaming computations can be run on any parallel machine which supports MPI; the latter allows them to run on a heterogeneous, geographically dispersed network of machines. We illustrate how PHISH can support streaming MapReduce operations, and describe streaming versions of three algorithms for large, sparse graph analytics: triangle enumeration, subgraph isomorphism matching, and connected component finding. Lastly, we also provide benchmark timings for MPI versus socket performance of several kernel operations useful in streaming algorithms.« less

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

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).

Dynamic Load Balancing for Adaptive Computations on Distributed-Memory Machines

NASA Technical Reports Server (NTRS)

1999-01-01

Dynamic load balancing is central to adaptive mesh-based computations on large-scale parallel computers. The principal investigator has investigated various issues on the dynamic load balancing problem under NASA JOVE and JAG rants. The major accomplishments of the project are two graph partitioning algorithms and a load balancing framework. The S-HARP dynamic graph partitioner is known to be the fastest among the known dynamic graph partitioners to date. It can partition a graph of over 100,000 vertices in 0.25 seconds on a 64- processor Cray T3E distributed-memory multiprocessor while maintaining the scalability of over 16-fold speedup. Other known and widely used dynamic graph partitioners take over a second or two while giving low scalability of a few fold speedup on 64 processors. These results have been published in journals and peer-reviewed flagship conferences.

Unsupervised chunking based on graph propagation from bilingual corpus.

PubMed

Zhu, Ling; Wong, Derek F; Chao, Lidia S

2014-01-01

This paper presents a novel approach for unsupervised shallow parsing model trained on the unannotated Chinese text of parallel Chinese-English corpus. In this approach, no information of the Chinese side is applied. The exploitation of graph-based label propagation for bilingual knowledge transfer, along with an application of using the projected labels as features in unsupervised model, contributes to a better performance. The experimental comparisons with the state-of-the-art algorithms show that the proposed approach is able to achieve impressive higher accuracy in terms of F-score.

Efficient sequential and parallel algorithms for record linkage

PubMed Central

Mamun, Abdullah-Al; Mi, Tian; Aseltine, Robert; Rajasekaran, Sanguthevar

2014-01-01

Background and objective Integrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms. Methods Our algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components. Results Our sequential and parallel algorithms have been tested on a real dataset of 1 083 878 records and synthetic datasets ranging in size from 50 000 to 9 000 000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes). Conclusions We have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm. PMID:24154837

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.

Overlapping clusters for distributed computation.

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

Mirrokni, Vahab; Andersen, Reid; Gleich, David F.

2010-11-01

Scalable, distributed algorithms must address communication problems. We investigate overlapping clusters, or vertex partitions that intersect, for graph computations. This setup stores more of the graph than required but then affords the ease of implementation of vertex partitioned algorithms. Our hope is that this technique allows us to reduce communication in a computation on a distributed graph. The motivation above draws on recent work in communication avoiding algorithms. Mohiyuddin et al. (SC09) design a matrix-powers kernel that gives rise to an overlapping partition. Fritzsche et al. (CSC2009) develop an overlapping clustering for a Schwarz method. Both techniques extend an initialmore » partitioning with overlap. Our procedure generates overlap directly. Indeed, Schwarz methods are commonly used to capitalize on overlap. Elsewhere, overlapping communities (Ahn et al, Nature 2009; Mishra et al. WAW2007) are now a popular model of structure in social networks. These have long been studied in statistics (Cole and Wishart, CompJ 1970). We present two types of results: (i) an estimated swapping probability {rho}{infinity}; and (ii) the communication volume of a parallel PageRank solution (link-following {alpha} = 0.85) using an additive Schwarz method. The volume ratio is the amount of extra storage for the overlap (2 means we store the graph twice). Below, as the ratio increases, the swapping probability and PageRank communication volume decreases.« less

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.

User-Assisted Store Recycling for Dynamic Task Graph Schedulers

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

Kurt, Mehmet Can; Krishnamoorthy, Sriram; Agrawal, Gagan

The emergence of the multi-core era has led to increased interest in designing effective yet practical parallel programming models. Models based on task graphs that operate on single-assignment data are attractive in several ways: they can support dynamic applications and precisely represent the available concurrency. However, they also require nuanced algorithms for scheduling and memory management for efficient execution. In this paper, we consider memory-efficient dynamic scheduling of task graphs. Specifically, we present a novel approach for dynamically recycling the memory locations assigned to data items as they are produced by tasks. We develop algorithms to identify memory-efficient store recyclingmore » functions by systematically evaluating the validity of a set of (user-provided or automatically generated) alternatives. Because recycling function can be input data-dependent, we have also developed support for continued correct execution of a task graph in the presence of a potentially incorrect store recycling function. Experimental evaluation demonstrates that our approach to automatic store recycling incurs little to no overheads, achieves memory usage comparable to the best manually derived solutions, often produces recycling functions valid across problem sizes and input parameters, and efficiently recovers from an incorrect choice of store recycling functions.« less

Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1999-01-01

The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

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.

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

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

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George Widgery

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented onmore » both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.« less

Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

NASA Astrophysics Data System (ADS)

Endo, Eishin; Toga, Yuta; Sasaki, Munetaka

2015-07-01

We present a method of parallelizing the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide a lattice into noninteracting interpenetrating sublattices. This subdivision enables us to parallelize the Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. This method was applied to a two-dimensional magnetic dipolar system on an L × L square lattice to examine its parallelization efficiency. The result showed that, in the case of L = 2304, the speed of computation increased about 102 times by parallel computation with 288 processors.

Computer architecture for efficient algorithmic executions in real-time systems: New technology for avionics systems and advanced space vehicles

NASA Technical Reports Server (NTRS)

Carroll, Chester C.; Youngblood, John N.; Saha, Aindam

1987-01-01

Improvements and advances in the development of computer architecture now provide innovative technology for the recasting of traditional sequential solutions into high-performance, low-cost, parallel system to increase system performance. Research conducted in development of specialized computer architecture for the algorithmic execution of an avionics system, guidance and control problem in real time is described. A comprehensive treatment of both the hardware and software structures of a customized computer which performs real-time computation of guidance commands with updated estimates of target motion and time-to-go is presented. An optimal, real-time allocation algorithm was developed which maps the algorithmic tasks onto the processing elements. This allocation is based on the critical path analysis. The final stage is the design and development of the hardware structures suitable for the efficient execution of the allocated task graph. The processing element is designed for rapid execution of the allocated tasks. Fault tolerance is a key feature of the overall architecture. Parallel numerical integration techniques, tasks definitions, and allocation algorithms are discussed. The parallel implementation is analytically verified and the experimental results are presented. The design of the data-driven computer architecture, customized for the execution of the particular algorithm, is discussed.

Computer architecture for efficient algorithmic executions in real-time systems: new technology for avionics systems and advanced space vehicles

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

Carroll, C.C.; Youngblood, J.N.; Saha, A.

1987-12-01

Improvements and advances in the development of computer architecture now provide innovative technology for the recasting of traditional sequential solutions into high-performance, low-cost, parallel system to increase system performance. Research conducted in development of specialized computer architecture for the algorithmic execution of an avionics system, guidance and control problem in real time is described. A comprehensive treatment of both the hardware and software structures of a customized computer which performs real-time computation of guidance commands with updated estimates of target motion and time-to-go is presented. An optimal, real-time allocation algorithm was developed which maps the algorithmic tasks onto the processingmore » elements. This allocation is based on the critical path analysis. The final stage is the design and development of the hardware structures suitable for the efficient execution of the allocated task graph. The processing element is designed for rapid execution of the allocated tasks. Fault tolerance is a key feature of the overall architecture. Parallel numerical integration techniques, tasks definitions, and allocation algorithms are discussed. The parallel implementation is analytically verified and the experimental results are presented. The design of the data-driven computer architecture, customized for the execution of the particular algorithm, is discussed.« less

Methodes iteratives paralleles: Applications en neutronique et en mecanique des fluides

NASA Astrophysics Data System (ADS)

Qaddouri, Abdessamad

Dans cette these, le calcul parallele est applique successivement a la neutronique et a la mecanique des fluides. Dans chacune de ces deux applications, des methodes iteratives sont utilisees pour resoudre le systeme d'equations algebriques resultant de la discretisation des equations du probleme physique. Dans le probleme de neutronique, le calcul des matrices des probabilites de collision (PC) ainsi qu'un schema iteratif multigroupe utilisant une methode inverse de puissance sont parallelises. Dans le probleme de mecanique des fluides, un code d'elements finis utilisant un algorithme iteratif du type GMRES preconditionne est parallelise. Cette these est presentee sous forme de six articles suivis d'une conclusion. Les cinq premiers articles traitent des applications en neutronique, articles qui representent l'evolution de notre travail dans ce domaine. Cette evolution passe par un calcul parallele des matrices des PC et un algorithme multigroupe parallele teste sur un probleme unidimensionnel (article 1), puis par deux algorithmes paralleles l'un mutiregion l'autre multigroupe, testes sur des problemes bidimensionnels (articles 2--3). Ces deux premieres etapes sont suivies par l'application de deux techniques d'acceleration, le rebalancement neutronique et la minimisation du residu aux deux algorithmes paralleles (article 4). Finalement, on a mis en oeuvre l'algorithme multigroupe et le calcul parallele des matrices des PC sur un code de production DRAGON ou les tests sont plus realistes et peuvent etre tridimensionnels (article 5). Le sixieme article (article 6), consacre a l'application a la mecanique des fluides, traite la parallelisation d'un code d'elements finis FES ou le partitionneur de graphe METIS et la librairie PSPARSLIB sont utilises.

Superpixel-based graph cuts for accurate stereo matching

NASA Astrophysics Data System (ADS)

Feng, Liting; Qin, Kaihuai

2017-06-01

Estimating the surface normal vector and disparity of a pixel simultaneously, also known as three-dimensional label method, has been widely used in recent continuous stereo matching problem to achieve sub-pixel accuracy. However, due to the infinite label space, it’s extremely hard to assign each pixel an appropriate label. In this paper, we present an accurate and efficient algorithm, integrating patchmatch with graph cuts, to approach this critical computational problem. Besides, to get robust and precise matching cost, we use a convolutional neural network to learn a similarity measure on small image patches. Compared with other MRF related methods, our method has several advantages: its sub-modular property ensures a sub-problem optimality which is easy to perform in parallel; graph cuts can simultaneously update multiple pixels, avoiding local minima caused by sequential optimizers like belief propagation; it uses segmentation results for better local expansion move; local propagation and randomization can easily generate the initial solution without using external methods. Middlebury experiments show that our method can get higher accuracy than other MRF-based algorithms.

Numerical characteristics of quantum computer simulation

NASA Astrophysics Data System (ADS)

Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.

2016-12-01

The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.

Efficient Synthesis of Graph Methods: a Dynamically Scheduled Architecture

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

Minutoli, Marco; Castellana, Vito G.; Tumeo, Antonino

RDF databases naturally map to a graph representation and employ languages, such as SPARQL, that implements queries as graph pattern matching routines. Graph methods exhibit an irregular behavior: they present unpredictable, fine-grained data accesses, and are synchronization inten- sive. Graph data structures expose large amounts of dy- namic parallelism, but are difficult to partition without gen- erating load unbalance. In this paper, we present a novel ar- chitecture to improve the synthesis of graph methods. Our design addresses the issues of these algorithms with two com- ponents: a Dynamic Task Scheduler (DTS), which reduces load unbalance and maximize resource utilization,more » and a Hi- erarchical Memory Interface controller (HMI), which pro- vides support for concurrent memory operations on multi- ported/multi-banked shared memories. We evaluate our ap- proach by generating the accelerators for a set of SPARQL queries from the Lehigh University Benchmark (LUBM). We first analyze the load unbalance of these queries, showing that execution time among tasks can differ even of order of magnitudes. We then synthesize the queries and com- pare the performance of the resulting accelerators against the current state of the art. Experimental results show that our solution provides a speedup over the serial implementa- tion close to the theoretical maximum and a speedup up to 3.45 over a baseline parallel implementation. We conclude our study by exploring the design space to achieve maximum memory channels utilization. The best design used at least three of the four memory channels for more than 90% of the execution time.« less

Parallel multi-join query optimization algorithm for distributed sensor network in the internet of things

NASA Astrophysics Data System (ADS)

Zheng, Yan

2015-03-01

Internet of things (IoT), focusing on providing users with information exchange and intelligent control, attracts a lot of attention of researchers from all over the world since the beginning of this century. IoT is consisted of large scale of sensor nodes and data processing units, and the most important features of IoT can be illustrated as energy confinement, efficient communication and high redundancy. With the sensor nodes increment, the communication efficiency and the available communication band width become bottle necks. Many research work is based on the instance which the number of joins is less. However, it is not proper to the increasing multi-join query in whole internet of things. To improve the communication efficiency between parallel units in the distributed sensor network, this paper proposed parallel query optimization algorithm based on distribution attributes cost graph. The storage information relations and the network communication cost are considered in this algorithm, and an optimized information changing rule is established. The experimental result shows that the algorithm has good performance, and it would effectively use the resource of each node in the distributed sensor network. Therefore, executive efficiency of multi-join query between different nodes could be improved.

ASC-ATDM Performance Portability Requirements for 2015-2019

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

Edwards, Harold C.; Trott, Christian Robert

This report outlines the research, development, and support requirements for the Advanced Simulation and Computing (ASC ) Advanced Technology, Development, and Mitigation (ATDM) Performance Portability (a.k.a., Kokkos) project for 2015 - 2019 . The research and development (R&D) goal for Kokkos (v2) has been to create and demonstrate a thread - parallel programming model a nd standard C++ library - based implementation that enables performance portability across diverse manycore architectures such as multicore CPU, Intel Xeon Phi, and NVIDIA Kepler GPU. This R&D goal has been achieved for algorithms that use data parallel pat terns including parallel - for, parallelmore » - reduce, and parallel - scan. Current R&D is focusing on hierarchical parallel patterns such as a directed acyclic graph (DAG) of asynchronous tasks where each task contain s nested data parallel algorithms. This five y ear plan includes R&D required to f ully and performance portably exploit thread parallelism across current and anticipated next generation platforms (NGP). The Kokkos library is being evaluated by many projects exploring algorithm s and code design for NGP. Some production libraries and applications such as Trilinos and LAMMPS have already committed to Kokkos as their foundation for manycore parallelism an d performance portability. These five year requirements includes support required for current and antic ipated ASC projects to be effective and productive in their use of Kokkos on NGP. The greatest risk to the success of Kokkos and ASC projects relying upon Kokkos is a lack of staffing resources to support Kokkos to the degree needed by these ASC projects. This support includes up - to - date tutorials, documentation, multi - platform (hardware and software stack) testing, minor feature enhancements, thread - scalable algorithm consulting, and managing collaborative R&D.« less

Composing Data Parallel Code for a SPARQL Graph Engine

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

Castellana, Vito G.; Tumeo, Antonino; Villa, Oreste

Big data analytics process large amount of data to extract knowledge from them. Semantic databases are big data applications that adopt the Resource Description Framework (RDF) to structure metadata through a graph-based representation. The graph based representation provides several benefits, such as the possibility to perform in memory processing with large amounts of parallelism. SPARQL is a language used to perform queries on RDF-structured data through graph matching. In this paper we present a tool that automatically translates SPARQL queries to parallel graph crawling and graph matching operations. The tool also supports complex SPARQL constructs, which requires more than basicmore » graph matching for their implementation. The tool generates parallel code annotated with OpenMP pragmas for x86 Shared-memory Multiprocessors (SMPs). With respect to commercial database systems such as Virtuoso, our approach reduces memory occupation due to join operations and provides higher performance. We show the scaling of the automatically generated graph-matching code on a 48-core SMP.« less

Algorithms for Automatic Alignment of Arrays

NASA Technical Reports Server (NTRS)

Chatterjee, Siddhartha; Gilbert, John R.; Oliker, Leonid; Schreiber, Robert; Sheffler, Thomas J.

1996-01-01

Aggregate data objects (such as arrays) are distributed across the processor memories when compiling a data-parallel language for a distributed-memory machine. The mapping determines the amount of communication needed to bring operands of parallel operations into alignment with each other. A common approach is to break the mapping into two stages: an alignment that maps all the objects to an abstract template, followed by a distribution that maps the template to the processors. This paper describes algorithms for solving the various facets of the alignment problem: axis and stride alignment, static and mobile offset alignment, and replication labeling. We show that optimal axis and stride alignment is NP-complete for general program graphs, and give a heuristic method that can explore the space of possible solutions in a number of ways. We show that some of these strategies can give better solutions than a simple greedy approach proposed earlier. We also show how local graph contractions can reduce the size of the problem significantly without changing the best solution. This allows more complex and effective heuristics to be used. We show how to model the static offset alignment problem using linear programming, and we show that loop-dependent mobile offset alignment is sometimes necessary for optimum performance. We describe an algorithm with for determining mobile alignments for objects within do loops. We also identify situations in which replicated alignment is either required by the program itself or can be used to improve performance. We describe an algorithm based on network flow that replicates objects so as to minimize the total amount of broadcast communication in replication.

GBS 1.0

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

2010-09-30

The Umbra gbs (Graph-Based Search) library provides implementations of graph-based search/planning algorithms that can be applied to legacy graph data structures. Unlike some other graph algorithm libraries, this one does not require your graph class to inherit from a specific base class. Implementations of Dijkstra's Algorithm and A-Star search are included and can be used with graphs that are lazily-constructed.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure

NASA Astrophysics Data System (ADS)

Ciandrini, L.; Maffi, C.; Motta, A.; Bassetti, B.; Cosentino Lagomarsino, M.

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter γ . We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying γ , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure.

PubMed

Ciandrini, L; Maffi, C; Motta, A; Bassetti, B; Cosentino Lagomarsino, M

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying gamma , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Automatic Data Distribution for CFD Applications on Structured Grids

NASA Technical Reports Server (NTRS)

Frumkin, Michael; Yan, Jerry

2000-01-01

Data distribution is an important step in implementation of any parallel algorithm. The data distribution determines data traffic, utilization of the interconnection network and affects the overall code efficiency. In recent years a number data distribution methods have been developed and used in real programs for improving data traffic. We use some of the methods for translating data dependence and affinity relations into data distribution directives. We describe an automatic data alignment and placement tool (ADAFT) which implements these methods and show it results for some CFD codes (NPB and ARC3D). Algorithms for program analysis and derivation of data distribution implemented in ADAFT are efficient three pass algorithms. Most algorithms have linear complexity with the exception of some graph algorithms having complexity O(n(sup 4)) in the worst case.

Automatic Data Distribution for CFD Applications on Structured Grids

NASA Technical Reports Server (NTRS)

Frumkin, Michael; Yan, Jerry

1999-01-01

Data distribution is an important step in implementation of any parallel algorithm. The data distribution determines data traffic, utilization of the interconnection network and affects the overall code efficiency. In recent years a number data distribution methods have been developed and used in real programs for improving data traffic. We use some of the methods for translating data dependence and affinity relations into data distribution directives. We describe an automatic data alignment and placement tool (ADAPT) which implements these methods and show it results for some CFD codes (NPB and ARC3D). Algorithms for program analysis and derivation of data distribution implemented in ADAPT are efficient three pass algorithms. Most algorithms have linear complexity with the exception of some graph algorithms having complexity O(n(sup 4)) in the worst case.

A unified framework for building high performance DVEs

NASA Astrophysics Data System (ADS)

Lei, Kaibin; Ma, Zhixia; Xiong, Hua

2011-10-01

A unified framework for integrating PC cluster based parallel rendering with distributed virtual environments (DVEs) is presented in this paper. While various scene graphs have been proposed in DVEs, it is difficult to enable collaboration of different scene graphs. This paper proposes a technique for non-distributed scene graphs with the capability of object and event distribution. With the increase of graphics data, DVEs require more powerful rendering ability. But general scene graphs are inefficient in parallel rendering. The paper also proposes a technique to connect a DVE and a PC cluster based parallel rendering environment. A distributed multi-player video game is developed to show the interaction of different scene graphs and the parallel rendering performance on a large tiled display wall.

A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

DTIC Science & Technology

2015-05-01

collaborative effort “ Adiabatic Quantum Computing Applications Research” (14-RI-CRADA-02) between the Information Directorate and Lock- 3 Algorithm 3...using Matlab, a quantum annealing approach using the D-Wave computer , and lastly using satisfiability modulo theory (SMT) and corresponding SMT...methods are explored and consist of a parallel computing approach using Matlab, a quantum annealing approach using the D-Wave computer , and lastly using

Artificial Intelligence (Al) Center of Excellence at the University of Pennsylvania

DTIC Science & Technology

1995-07-01

Approach and repel behaviors were implemented in order to study higher level behavioral simulation . Parallel algorithms for motion planning (as a...of decision-making accuracy can be specified for this graph-reduction process. We have also developed a mixed qualitative/quantitative simulation ...system, called QobiSIM. QobiSIM has been used to develop a cardiovascular simulation to be incorporated into the TraumAID system. This cardiovascular

Thought Leaders during Crises in Massive Social Networks

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

Corley, Courtney D.; Farber, Robert M.; Reynolds, William

The vast amount of social media data that can be gathered from the internet coupled with workflows that utilize both commodity systems and massively parallel supercomputers, such as the Cray XMT, open new vistas for research to support health, defense, and national security. Computer technology now enables the analysis of graph structures containing more than 4 billion vertices joined by 34 billion edges along with metrics and massively parallel algorithms that exhibit near-linear scalability according to number of processors. The challenge lies in making this massive data and analysis comprehensible to an analyst and end-users that require actionable knowledge tomore » carry out their duties. Simply stated, we have developed language and content agnostic techniques to reduce large graphs built from vast media corpora into forms people can understand. Specifically, our tools and metrics act as a survey tool to identify thought leaders' -- those members that lead or reflect the thoughts and opinions of an online community, independent of the source language.« less

Properties of the numerical algorithms for problems of quantum information technologies: Benefits of deep analysis

NASA Astrophysics Data System (ADS)

Chernyavskiy, Andrey; Khamitov, Kamil; Teplov, Alexey; Voevodin, Vadim; Voevodin, Vladimir

2016-10-01

In recent years, quantum information technologies (QIT) showed great development, although, the way of the implementation of QIT faces the serious difficulties, some of which are challenging computational tasks. This work is devoted to the deep and broad analysis of the parallel algorithmic properties of such tasks. As an example we take one- and two-qubit transformations of a many-qubit quantum state, which are the most critical kernels of many important QIT applications. The analysis of the algorithms uses the methodology of the AlgoWiki project (algowiki-project.org) and consists of two parts: theoretical and experimental. Theoretical part includes features like sequential and parallel complexity, macro structure, and visual information graph. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia) and includes the analysis of locality and memory access, scalability and the set of more specific dynamic characteristics of realization. This approach allowed us to obtain bottlenecks and generate ideas of efficiency improvement.

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.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

Massively Multithreaded Maxflow for Image Segmentation on the Cray XMT-2

PubMed Central

Bokhari, Shahid H.; Çatalyürek, Ümit V.; Gurcan, Metin N.

2014-01-01

SUMMARY Image segmentation is a very important step in the computerized analysis of digital images. The maxflow mincut approach has been successfully used to obtain minimum energy segmentations of images in many fields. Classical algorithms for maxflow in networks do not directly lend themselves to efficient parallel implementations on contemporary parallel processors. We present the results of an implementation of Goldberg-Tarjan preflow-push algorithm on the Cray XMT-2 massively multithreaded supercomputer. This machine has hardware support for 128 threads in each physical processor, a uniformly accessible shared memory of up to 4 TB and hardware synchronization for each 64 bit word. It is thus well-suited to the parallelization of graph theoretic algorithms, such as preflow-push. We describe the implementation of the preflow-push code on the XMT-2 and present the results of timing experiments on a series of synthetically generated as well as real images. Our results indicate very good performance on large images and pave the way for practical applications of this machine architecture for image analysis in a production setting. The largest images we have run are 320002 pixels in size, which are well beyond the largest previously reported in the literature. PMID:25598745

Proceedings: Sisal `93

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

Feo, J.T.

1993-10-01

This report contain papers on: Programmability and performance issues; The case of an iterative partial differential equation solver; Implementing the kernal of the Australian Region Weather Prediction Model in Sisal; Even and quarter-even prime length symmetric FFTs and their Sisal Implementations; Top-down thread generation for Sisal; Overlapping communications and computations on NUMA architechtures; Compiling technique based on dataflow analysis for funtional programming language Valid; Copy elimination for true multidimensional arrays in Sisal 2.0; Increasing parallelism for an optimization that reduces copying in IF2 graphs; Caching in on Sisal; Cache performance of Sisal Vs. FORTRAN; FFT algorithms on a shared-memory multiprocessor;more » A parallel implementation of nonnumeric search problems in Sisal; Computer vision algorithms in Sisal; Compilation of Sisal for a high-performance data driven vector processor; Sisal on distributed memory machines; A virtual shared addressing system for distributed memory Sisal; Developing a high-performance FFT algorithm in Sisal for a vector supercomputer; Implementation issues for IF2 on a static data-flow architechture; and Systematic control of parallelism in array-based data-flow computation. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.« less

A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.

1990-01-01

While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.

A distributed query execution engine of big attributed graphs.

PubMed

Batarfi, Omar; Elshawi, Radwa; Fayoumi, Ayman; Barnawi, Ahmed; Sakr, Sherif

2016-01-01

A graph is a popular data model that has become pervasively used for modeling structural relationships between objects. In practice, in many real-world graphs, the graph vertices and edges need to be associated with descriptive attributes. Such type of graphs are referred to as attributed graphs. G-SPARQL has been proposed as an expressive language, with a centralized execution engine, for querying attributed graphs. G-SPARQL supports various types of graph querying operations including reachability, pattern matching and shortest path where any G-SPARQL query may include value-based predicates on the descriptive information (attributes) of the graph edges/vertices in addition to the structural predicates. In general, a main limitation of centralized systems is that their vertical scalability is always restricted by the physical limits of computer systems. This article describes the design, implementation in addition to the performance evaluation of DG-SPARQL, a distributed, hybrid and adaptive parallel execution engine of G-SPARQL queries. In this engine, the topology of the graph is distributed over the main memory of the underlying nodes while the graph data are maintained in a relational store which is replicated on the disk of each of the underlying nodes. DG-SPARQL evaluates parts of the query plan via SQL queries which are pushed to the underlying relational stores while other parts of the query plan, as necessary, are evaluated via indexless memory-based graph traversal algorithms. Our experimental evaluation shows the efficiency and the scalability of DG-SPARQL on querying massive attributed graph datasets in addition to its ability to outperform the performance of Apache Giraph, a popular distributed graph processing system, by orders of magnitudes.

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.

Efficient Graph Based Assembly of Short-Read Sequences on Hybrid Core Architecture

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

Sczyrba, Alex; Pratap, Abhishek; Canon, Shane

2011-03-22

Advanced architectures can deliver dramatically increased throughput for genomics and proteomics applications, reducing time-to-completion in some cases from days to minutes. One such architecture, hybrid-core computing, marries a traditional x86 environment with a reconfigurable coprocessor, based on field programmable gate array (FPGA) technology. In addition to higher throughput, increased performance can fundamentally improve research quality by allowing more accurate, previously impractical approaches. We will discuss the approach used by Convey?s de Bruijn graph constructor for short-read, de-novo assembly. Bioinformatics applications that have random access patterns to large memory spaces, such as graph-based algorithms, experience memory performance limitations on cache-based x86more » servers. Convey?s highly parallel memory subsystem allows application-specific logic to simultaneously access 8192 individual words in memory, significantly increasing effective memory bandwidth over cache-based memory systems. Many algorithms, such as Velvet and other de Bruijn graph based, short-read, de-novo assemblers, can greatly benefit from this type of memory architecture. Furthermore, small data type operations (four nucleotides can be represented in two bits) make more efficient use of logic gates than the data types dictated by conventional programming models.JGI is comparing the performance of Convey?s graph constructor and Velvet on both synthetic and real data. We will present preliminary results on memory usage and run time metrics for various data sets with different sizes, from small microbial and fungal genomes to very large cow rumen metagenome. For genomes with references we will also present assembly quality comparisons between the two assemblers.« less

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

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

Deveci, Mehmet; Trott, Christian Robert; Rajamanickam, Sivasankaran

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures.

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

Deveci, Mehmet; Rajamanickam, Sivasankaran; Trott, Christian Robert

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scienti c computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Accelerating the Mining of Influential Nodes in Complex Networks through Community Detection

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

Halappanavar, Mahantesh; Sathanur, Arun V.; Nandi, Apurba

Computing the set of influential nodes with a given size to ensure maximal spread of influence on a complex network is a challenging problem impacting multiple applications. A rigorous approach to influence maximization involves utilization of optimization routines that comes with a high computational cost. In this work, we propose to exploit the existence of communities in complex networks to accelerate the mining of influential seeds. We provide intuitive reasoning to explain why our approach should be able to provide speedups without significantly degrading the extent of the spread of influence when compared to the case of influence maximization withoutmore » using the community information. Additionally, we have parallelized the complete workflow by leveraging an existing parallel implementation of the Louvain community detection algorithm. We then conduct a series of experiments on a dataset with three representative graphs to first verify our implementation and then demonstrate the speedups. Our method achieves speedups ranging from 3x - 28x for graphs with small number of communities while nearly matching or even exceeding the activation performance on the entire graph. Complexity analysis reveals that dramatic speedups are possible for larger graphs that contain a correspondingly larger number of communities. In addition to the speedups obtained from the utilization of the community structure, scalability results show up to 6.3x speedup on 20 cores relative to the baseline run on 2 cores. Finally, current limitations of the approach are outlined along with the planned next steps.« 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

Wasatch: An architecture-proof multiphysics development environment using a Domain Specific Language and graph theory

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

Saad, Tony; Sutherland, James C.

To address the coding and software challenges of modern hybrid architectures, we propose an approach to multiphysics code development for high-performance computing. This approach is based on using a Domain Specific Language (DSL) in tandem with a directed acyclic graph (DAG) representation of the problem to be solved that allows runtime algorithm generation. When coupled with a large-scale parallel framework, the result is a portable development framework capable of executing on hybrid platforms and handling the challenges of multiphysics applications. In addition, we share our experience developing a code in such an environment – an effort that spans an interdisciplinarymore » team of engineers and computer scientists.« less

Wasatch: An architecture-proof multiphysics development environment using a Domain Specific Language and graph theory

DOE PAGES

Saad, Tony; Sutherland, James C.

2016-05-04

To address the coding and software challenges of modern hybrid architectures, we propose an approach to multiphysics code development for high-performance computing. This approach is based on using a Domain Specific Language (DSL) in tandem with a directed acyclic graph (DAG) representation of the problem to be solved that allows runtime algorithm generation. When coupled with a large-scale parallel framework, the result is a portable development framework capable of executing on hybrid platforms and handling the challenges of multiphysics applications. In addition, we share our experience developing a code in such an environment – an effort that spans an interdisciplinarymore » team of engineers and computer scientists.« 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.

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

Algorithms and software used in selecting structure of machine-training cluster based on neurocomputers

NASA Astrophysics Data System (ADS)

Romanchuk, V. A.; Lukashenko, V. V.

2018-05-01

The technique of functioning of a control system by a computing cluster based on neurocomputers is proposed. Particular attention is paid to the method of choosing the structure of the computing cluster due to the fact that the existing methods are not effective because of a specialized hardware base - neurocomputers, which are highly parallel computer devices with an architecture different from the von Neumann architecture. A developed algorithm for choosing the computational structure of a cloud cluster is described, starting from the direction of data transfer in the flow control graph of the program and its adjacency matrix.

Enhancing data locality by using terminal propagation

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

Hendrickson, B.; Leland, R.; Van Driessche, R.

1995-12-31

Terminal propagation is a method developed in the circuit placement community for adding constraints to graph partitioning problems. This paper adapts and expands this idea, and applies it to the problem of partitioning data structures among the processors of a parallel computer. We show how the constraints in terminal propagation can be used to encourage partitions in which messages are communicated only between architecturally near processors. We then show how these constraints can be handled in two important partitioning algorithms, spectral bisection and multilevel-KL. We compare the quality of partitions generated by these algorithms to each other and to Partitionsmore » generated by more familiar techniques.« less

AgRISTARS. Supporting research: Algorithms for scene modelling

NASA Technical Reports Server (NTRS)

Rassbach, M. E. (Principal Investigator)

1982-01-01

The requirements for a comprehensive analysis of LANDSAT or other visual data scenes are defined. The development of a general model of a scene and a computer algorithm for finding the particular model for a given scene is discussed. The modelling system includes a boundary analysis subsystem, which detects all the boundaries and lines in the image and builds a boundary graph; a continuous variation analysis subsystem, which finds gradual variations not well approximated by a boundary structure; and a miscellaneous features analysis, which includes texture, line parallelism, etc. The noise reduction capabilities of this method and its use in image rectification and registration are discussed.

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.

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

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.

Reducing False Positives in Runtime Analysis of Deadlocks

NASA Technical Reports Server (NTRS)

Bensalem, Saddek; Havelund, Klaus; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper presents an improvement of a standard algorithm for detecting dead-lock potentials in multi-threaded programs, in that it reduces the number of false positives. The standard algorithm works as follows. The multi-threaded program under observation is executed, while lock and unlock events are observed. A graph of locks is built, with edges between locks symbolizing locking orders. Any cycle in the graph signifies a potential for a deadlock. The typical standard example is the group of dining philosophers sharing forks. The algorithm is interesting because it can catch deadlock potentials even though no deadlocks occur in the examined trace, and at the same time it scales very well in contrast t o more formal approaches to deadlock detection. The algorithm, however, can yield false positives (as well as false negatives). The extension of the algorithm described in this paper reduces the amount of false positives for three particular cases: when a gate lock protects a cycle, when a single thread introduces a cycle, and when the code segments in different threads that cause the cycle can actually not execute in parallel. The paper formalizes a theory for dynamic deadlock detection and compares it to model checking and static analysis techniques. It furthermore describes an implementation for analyzing Java programs and its application to two case studies: a planetary rover and a space craft altitude control system.

A Faster Parallel Algorithm and Efficient Multithreaded Implementations for Evaluating Betweenness Centrality on Massive Datasets

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

Madduri, Kamesh; Ediger, David; Jiang, Karl

2009-02-15

We present a new lock-free parallel algorithm for computing betweenness centralityof massive small-world networks. With minor changes to the data structures, ouralgorithm also achieves better spatial cache locality compared to previous approaches. Betweenness centrality is a key algorithm kernel in HPCS SSCA#2, a benchmark extensively used to evaluate the performance of emerging high-performance computing architectures for graph-theoretic computations. We design optimized implementations of betweenness centrality and the SSCA#2 benchmark for two hardware multithreaded systems: a Cray XMT system with the Threadstorm processor, and a single-socket Sun multicore server with the UltraSPARC T2 processor. For a small-world network of 134 millionmore » vertices and 1.073 billion edges, the 16-processor XMT system and the 8-core Sun Fire T5120 server achieve TEPS scores (an algorithmic performance count for the SSCA#2 benchmark) of 160 million and 90 million respectively, which corresponds to more than a 2X performance improvement over the previous parallel implementations. To better characterize the performance of these multithreaded systems, we correlate the SSCA#2 performance results with data from the memory-intensive STREAM and RandomAccess benchmarks. Finally, we demonstrate the applicability of our implementation to analyze massive real-world datasets by computing approximate betweenness centrality for a large-scale IMDb movie-actor network.« less

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.

Evaluation of concurrent priority queue algorithms. Technical report

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

Huang, Q.

1991-02-01

The priority queue is a fundamental data structure that is used in a large variety of parallel algorithms, such as multiprocessor scheduling and parallel best-first search of state-space graphs. This thesis addresses the design and experimental evaluation of two novel concurrent priority queues: a parallel Fibonacci heap and a concurrent priority pool, and compares them with the concurrent binary heap. The parallel Fibonacci heap is based on the sequential Fibonacci heap, which is theoretically the most efficient data structure for sequential priority queues. This scheme not only preserves the efficient operation time bounds of its sequential counterpart, but also hasmore » very low contention by distributing locks over the entire data structure. The experimental results show its linearly scalable throughput and speedup up to as many processors as tested (currently 18). A concurrent access scheme for a doubly linked list is described as part of the implementation of the parallel Fibonacci heap. The concurrent priority pool is based on the concurrent B-tree and the concurrent pool. The concurrent priority pool has the highest throughput among the priority queues studied. Like the parallel Fibonacci heap, the concurrent priority pool scales linearly up to as many processors as tested. The priority queues are evaluated in terms of throughput and speedup. Some applications of concurrent priority queues such as the vertex cover problem and the single source shortest path problem are tested.« less

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.

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

2017-10-01

We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

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.

Hypergraph partitioning implementation for parallelizing matrix-vector multiplication using CUDA GPU-based parallel computing

NASA Astrophysics Data System (ADS)

Murni, Bustamam, A.; Ernastuti, Handhika, T.; Kerami, D.

2017-07-01

Calculation of the matrix-vector multiplication in the real-world problems often involves large matrix with arbitrary size. Therefore, parallelization is needed to speed up the calculation process that usually takes a long time. Graph partitioning techniques that have been discussed in the previous studies cannot be used to complete the parallelized calculation of matrix-vector multiplication with arbitrary size. This is due to the assumption of graph partitioning techniques that can only solve the square and symmetric matrix. Hypergraph partitioning techniques will overcome the shortcomings of the graph partitioning technique. This paper addresses the efficient parallelization of matrix-vector multiplication through hypergraph partitioning techniques using CUDA GPU-based parallel computing. CUDA (compute unified device architecture) is a parallel computing platform and programming model that was created by NVIDIA and implemented by the GPU (graphics processing unit).

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

OpenMP Parallelization and Optimization of Graph-based Machine Learning Algorithms

DTIC Science & Technology

2016-05-01

composed of hyper - spectral video sequences recording the release of chemical plumes at the Dugway Proving Ground. We use the 329 frames of the...video. Each frame is a hyper - spectral image with dimension 128 × 320 × 129, where 129 is the dimension of the channel of each pixel. The total number of...j=1 . Then we use the nested for- loop to calculate the values of WXY by the formula (1). We then put the corresponding value in an array which

On k-ary n-cubes: Theory and applications

NASA Technical Reports Server (NTRS)

Mao, Weizhen; Nicol, David M.

1994-01-01

Many parallel processing networks can be viewed as graphs called k-ary n-cubes, whose special cases include rings, hypercubes and toruses. In this paper, combinatorial properties of k-ary n-cubes are explored. In particular, the problem of characterizing the subgraph of a given number of nodes with the maximum edge count is studied. These theoretical results are then used to compute a lower bounding function in branch-and-bound partitioning algorithms and to establish the optimality of some irregular partitions.

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.

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.

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.

Nonpreemptive run-time scheduling issues on a multitasked, multiprogrammed multiprocessor with dependencies, bidimensional tasks, folding and dynamic graphs

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

Miller, Allan Ray

1987-05-01

Increases in high speed hardware have mandated studies in software techniques to exploit the parallel capabilities. This thesis examines the effects a run-time scheduler has on a multiprocessor. The model consists of directed, acyclic graphs, generated from serial FORTRAN benchmark programs by the parallel compiler Parafrase. A multitasked, multiprogrammed environment is created. Dependencies are generated by the compiler. Tasks are bidimensional, i.e., they may specify both time and processor requests. Processor requests may be folded into execution time by the scheduler. The graphs may arrive at arbitrary time intervals. The general case is NP-hard, thus, a variety of heuristics aremore » examined by a simulator. Multiprogramming demonstrates a greater need for a run-time scheduler than does monoprogramming for a variety of reasons, e.g., greater stress on the processors, a larger number of independent control paths, more variety in the task parameters, etc. The dynamic critical path series of algorithms perform well. Dynamic critical volume did not add much. Unfortunately, dynamic critical path maximizes turnaround time as well as throughput. Two schedulers are presented which balance throughput and turnaround time. The first requires classification of jobs by type; the second requires selection of a ratio value which is dependent upon system parameters. 45 refs., 19 figs., 20 tabs.« less

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

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.

Parallel design patterns for a low-power, software-defined compressed video encoder

NASA Astrophysics Data System (ADS)

Bruns, Michael W.; Hunt, Martin A.; Prasad, Durga; Gunupudi, Nageswara R.; Sonachalam, Sekar

2011-06-01

Video compression algorithms such as H.264 offer much potential for parallel processing that is not always exploited by the technology of a particular implementation. Consumer mobile encoding devices often achieve real-time performance and low power consumption through parallel processing in Application Specific Integrated Circuit (ASIC) technology, but many other applications require a software-defined encoder. High quality compression features needed for some applications such as 10-bit sample depth or 4:2:2 chroma format often go beyond the capability of a typical consumer electronics device. An application may also need to efficiently combine compression with other functions such as noise reduction, image stabilization, real time clocks, GPS data, mission/ESD/user data or software-defined radio in a low power, field upgradable implementation. Low power, software-defined encoders may be implemented using a massively parallel memory-network processor array with 100 or more cores and distributed memory. The large number of processor elements allow the silicon device to operate more efficiently than conventional DSP or CPU technology. A dataflow programming methodology may be used to express all of the encoding processes including motion compensation, transform and quantization, and entropy coding. This is a declarative programming model in which the parallelism of the compression algorithm is expressed as a hierarchical graph of tasks with message communication. Data parallel and task parallel design patterns are supported without the need for explicit global synchronization control. An example is described of an H.264 encoder developed for a commercially available, massively parallel memorynetwork processor device.

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

Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

NASA Astrophysics Data System (ADS)

Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

2017-12-01

Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

GraphCrunch 2: Software tool for network modeling, alignment and clustering.

PubMed

Kuchaiev, Oleksii; Stevanović, Aleksandar; Hayes, Wayne; Pržulj, Nataša

2011-01-19

Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, GraphCruch 2 implements an algorithm for clustering nodes within a network based solely on their topological similarities. Using GraphCrunch 2, we demonstrate that eukaryotic and viral PPI networks may belong to different graph model families and show that topology-based clustering can reveal important functional similarities between proteins within yeast and human PPI networks. GraphCrunch 2 is a software tool that implements the latest research on biological network analysis. It parallelizes computationally intensive tasks to fully utilize the potential of modern multi-core CPUs. It is open-source and freely available for research use. It runs under the Windows and Linux platforms.

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.

I/O-Efficient Scientific Computation Using TPIE

NASA Technical Reports Server (NTRS)

Vengroff, Darren Erik; Vitter, Jeffrey Scott

1996-01-01

In recent years, input/output (I/O)-efficient algorithms for a wide variety of problems have appeared in the literature. However, systems specifically designed to assist programmers in implementing such algorithms have remained scarce. TPIE is a system designed to support I/O-efficient paradigms for problems from a variety of domains, including computational geometry, graph algorithms, and scientific computation. The TPIE interface frees programmers from having to deal not only with explicit read and write calls, but also the complex memory management that must be performed for I/O-efficient computation. In this paper we discuss applications of TPIE to problems in scientific computation. We discuss algorithmic issues underlying the design and implementation of the relevant components of TPIE and present performance results of programs written to solve a series of benchmark problems using our current TPIE prototype. Some of the benchmarks we present are based on the NAS parallel benchmarks while others are of our own creation. We demonstrate that the central processing unit (CPU) overhead required to manage I/O is small and that even with just a single disk, the I/O overhead of I/O-efficient computation ranges from negligible to the same order of magnitude as CPU time. We conjecture that if we use a number of disks in parallel this overhead can be all but eliminated.

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

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.

EmptyHeaded: A Relational Engine for Graph Processing

PubMed Central

Aberger, Christopher R.; Tu, Susan; Olukotun, Kunle; Ré, Christopher

2016-01-01

There are two types of high-performance graph processing engines: low- and high-level engines. Low-level engines (Galois, PowerGraph, Snap) provide optimized data structures and computation models but require users to write low-level imperative code, hence ensuring that efficiency is the burden of the user. In high-level engines, users write in query languages like datalog (SociaLite) or SQL (Grail). High-level engines are easier to use but are orders of magnitude slower than the low-level graph engines. We present EmptyHeaded, a high-level engine that supports a rich datalog-like query language and achieves performance comparable to that of low-level engines. At the core of EmptyHeaded’s design is a new class of join algorithms that satisfy strong theoretical guarantees but have thus far not achieved performance comparable to that of specialized graph processing engines. To achieve high performance, EmptyHeaded introduces a new join engine architecture, including a novel query optimizer and data layouts that leverage single-instruction multiple data (SIMD) parallelism. With this architecture, EmptyHeaded outperforms high-level approaches by up to three orders of magnitude on graph pattern queries, PageRank, and Single-Source Shortest Paths (SSSP) and is an order of magnitude faster than many low-level baselines. We validate that EmptyHeaded competes with the best-of-breed low-level engine (Galois), achieving comparable performance on PageRank and at most 3× worse performance on SSSP. PMID:28077912

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.

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 Robust Concurrent Approach for Road Extraction and Urbanization Monitoring Based on Superpixels Acquired from Spectral Remote Sensing Images

NASA Astrophysics Data System (ADS)

Seppke, Benjamin; Dreschler-Fischer, Leonie; Wilms, Christian

2016-08-01

The extraction of road signatures from remote sensing images as a promising indicator for urbanization is a classical segmentation problem. However, some segmentation algorithms often lead to non-sufficient results. One way to overcome this problem is the usage of superpixels, that represent a locally coherent cluster of connected pixels. Superpixels allow flexible, highly adaptive segmentation approaches due to the possibility of merging as well as splitting and form new basic image entities. On the other hand, superpixels require an appropriate representation containing all relevant information about topology and geometry to maximize their advantages.In this work, we present a combined geometric and topological representation based on a special graph representation, the so-called RS-graph. Moreover, we present the use of the RS-graph by means of a case study: the extraction of partially occluded road networks in rural areas from open source (spectral) remote sensing images by tracking. In addition, multiprocessing and GPU-based parallelization is used to speed up the construction of the representation and the application.

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

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.

One-dimensional swarm algorithm packaging

NASA Astrophysics Data System (ADS)

Lebedev, Boris K.; Lebedev, Oleg B.; Lebedeva, Ekaterina O.

2018-05-01

The paper considers an algorithm for solving the problem of onedimensional packaging based on the adaptive behavior model of an ant colony. The key role in the development of the ant algorithm is the choice of representation (interpretation) of the solution. The structure of the solution search graph, the procedure for finding solutions on the graph, the methods of deposition and evaporation of pheromone are described. Unlike the canonical paradigm of an ant algorithm, an ant on the solution search graph generates sets of elements distributed across blocks. Experimental studies were conducted on IBM PC. Compared with the existing algorithms, the results are improved.

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

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

Parallel tiled Nussinov RNA folding loop nest generated using both dependence graph transitive closure and loop skewing.

PubMed

Palkowski, Marek; Bielecki, Wlodzimierz

2017-06-02

RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the transitive closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.

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

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 Graph Based Backtracking Algorithm for Solving General CSPs

NASA Technical Reports Server (NTRS)

Pang, Wanlin; Goodwin, Scott D.

2003-01-01

Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.

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

Cohen, J; Dossa, D; Gokhale, M

Critical data science applications requiring frequent access to storage perform poorly on today's computing architectures. This project addresses efficient computation of data-intensive problems in national security and basic science by exploring, advancing, and applying a new form of computing called storage-intensive supercomputing (SISC). Our goal is to enable applications that simply cannot run on current systems, and, for a broad range of data-intensive problems, to deliver an order of magnitude improvement in price/performance over today's data-intensive architectures. This technical report documents much of the work done under LDRD 07-ERD-063 Storage Intensive Supercomputing during the period 05/07-09/07. The following chapters describe:more » (1) a new file I/O monitoring tool iotrace developed to capture the dynamic I/O profiles of Linux processes; (2) an out-of-core graph benchmark for level-set expansion of scale-free graphs; (3) an entity extraction benchmark consisting of a pipeline of eight components; and (4) an image resampling benchmark drawn from the SWarp program in the LSST data processing pipeline. The performance of the graph and entity extraction benchmarks was measured in three different scenarios: data sets residing on the NFS file server and accessed over the network; data sets stored on local disk; and data sets stored on the Fusion I/O parallel NAND Flash array. The image resampling benchmark compared performance of software-only to GPU-accelerated. In addition to the work reported here, an additional text processing application was developed that used an FPGA to accelerate n-gram profiling for language classification. The n-gram application will be presented at SC07 at the High Performance Reconfigurable Computing Technologies and Applications Workshop. The graph and entity extraction benchmarks were run on a Supermicro server housing the NAND Flash 40GB parallel disk array, the Fusion-io. The Fusion system specs are as follows: SuperMicro X7DBE Xeon Dual Socket Blackford Server Motherboard; 2 Intel Xeon Dual-Core 2.66 GHz processors; 1 GB DDR2 PC2-5300 RAM (2 x 512); 80GB Hard Drive (Seagate SATA II Barracuda). The Fusion board is presently capable of 4X in a PCIe slot. The image resampling benchmark was run on a dual Xeon workstation with NVIDIA graphics card (see Chapter 5 for full specification). An XtremeData Opteron+FPGA was used for the language classification application. We observed that these benchmarks are not uniformly I/O intensive. The only benchmark that showed greater that 50% of the time in I/O was the graph algorithm when it accessed data files over NFS. When local disk was used, the graph benchmark spent at most 40% of its time in I/O. The other benchmarks were CPU dominated. The image resampling benchmark and language classification showed order of magnitude speedup over software by using co-processor technology to offload the CPU-intensive kernels. Our experiments to date suggest that emerging hardware technologies offer significant benefit to boosting the performance of data-intensive algorithms. Using GPU and FPGA co-processors, we were able to improve performance by more than an order of magnitude on the benchmark algorithms, eliminating the processor bottleneck of CPU-bound tasks. Experiments with a prototype solid state nonvolative memory available today show 10X better throughput on random reads than disk, with a 2X speedup on a graph processing benchmark when compared to the use of local SATA disk.« 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.

Accelerating semantic graph databases on commodity clusters

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

Morari, Alessandro; Castellana, Vito G.; Haglin, David J.

We are developing a full software system for accelerating semantic graph databases on commodity cluster that scales to hundreds of nodes while maintaining constant query throughput. Our framework comprises a SPARQL to C++ compiler, a library of parallel graph methods and a custom multithreaded runtime layer, which provides a Partitioned Global Address Space (PGAS) programming model with fork/join parallelism and automatic load balancing over a commodity clusters. We present preliminary results for the compiler and for the runtime.

Connectivity algorithm with depth first search (DFS) on simple graphs

NASA Astrophysics Data System (ADS)

Riansanti, O.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to detect connectivity of a simple graph using Depth First Search (DFS). The DFS implementation in this paper differs than other research, that is, on counting the number of visited vertices. The algorithm obtains s from the number of vertices and visits source vertex, following by its adjacent vertices until the last vertex adjacent to the previous source vertex. Any simple graph is connected if s equals 0 and disconnected if s is greater than 0. The complexity of the algorithm is O(n2).

A topology visualization early warning distribution algorithm for large-scale network security incidents.

PubMed

He, Hui; Fan, Guotao; Ye, Jianwei; Zhang, Weizhe

2013-01-01

It is of great significance to research the early warning system for large-scale network security incidents. It can improve the network system's emergency response capabilities, alleviate the cyber attacks' damage, and strengthen the system's counterattack ability. A comprehensive early warning system is presented in this paper, which combines active measurement and anomaly detection. The key visualization algorithm and technology of the system are mainly discussed. The large-scale network system's plane visualization is realized based on the divide and conquer thought. First, the topology of the large-scale network is divided into some small-scale networks by the MLkP/CR algorithm. Second, the sub graph plane visualization algorithm is applied to each small-scale network. Finally, the small-scale networks' topologies are combined into a topology based on the automatic distribution algorithm of force analysis. As the algorithm transforms the large-scale network topology plane visualization problem into a series of small-scale network topology plane visualization and distribution problems, it has higher parallelism and is able to handle the display of ultra-large-scale network topology.

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.

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.

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.

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.

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.

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.

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

PuLP/XtraPuLP : Partitioning Tools for Extreme-Scale Graphs

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

Slota, George M; Rajamanickam, Sivasankaran; Madduri, Kamesh

2017-09-21

PuLP/XtraPulp is software for partitioning graphs from several real-world problems. Graphs occur in several places in real world from road networks, social networks and scientific simulations. For efficient parallel processing these graphs have to be partitioned (split) with respect to metrics such as computation and communication costs. Our software allows such partitioning for massive graphs.

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.

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

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.

A Hybrid Task Graph Scheduler for High Performance Image Processing Workflows.

PubMed

Blattner, Timothy; Keyrouz, Walid; Bhattacharyya, Shuvra S; Halem, Milton; Brady, Mary

2017-12-01

Designing applications for scalability is key to improving their performance in hybrid and cluster computing. Scheduling code to utilize parallelism is difficult, particularly when dealing with data dependencies, memory management, data motion, and processor occupancy. The Hybrid Task Graph Scheduler (HTGS) improves programmer productivity when implementing hybrid workflows for multi-core and multi-GPU systems. The Hybrid Task Graph Scheduler (HTGS) is an abstract execution model, framework, and API that increases programmer productivity when implementing hybrid workflows for such systems. HTGS manages dependencies between tasks, represents CPU and GPU memories independently, overlaps computations with disk I/O and memory transfers, keeps multiple GPUs occupied, and uses all available compute resources. Through these abstractions, data motion and memory are explicit; this makes data locality decisions more accessible. To demonstrate the HTGS application program interface (API), we present implementations of two example algorithms: (1) a matrix multiplication that shows how easily task graphs can be used; and (2) a hybrid implementation of microscopy image stitching that reduces code size by ≈ 43% compared to a manually coded hybrid workflow implementation and showcases the minimal overhead of task graphs in HTGS. Both of the HTGS-based implementations show good performance. In image stitching the HTGS implementation achieves similar performance to the hybrid workflow implementation. Matrix multiplication with HTGS achieves 1.3× and 1.8× speedup over the multi-threaded OpenBLAS library for 16k × 16k and 32k × 32k size matrices, respectively.

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.

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

SciSpark: In-Memory Map-Reduce for Earth Science Algorithms

NASA Astrophysics Data System (ADS)

Ramirez, P.; Wilson, B. D.; Whitehall, K. D.; Palamuttam, R. S.; Mattmann, C. A.; Shah, S.; Goodman, A.; Burke, W.

2016-12-01

We are developing a lightning fast Big Data technology called SciSpark based on ApacheTM Spark under a NASA AIST grant (PI Mattmann). Spark implements the map-reduce paradigm for parallel computing on a cluster, but emphasizes in-memory computation, "spilling" to disk only as needed, and so outperforms the disk-based Apache Hadoop by 100x in memory and by 10x on disk. SciSpark extends Spark to support Earth Science use in three ways: Efficient ingest of N-dimensional geo-located arrays (physical variables) from netCDF3/4, HDF4/5, and/or OPeNDAP URLS; Array operations for dense arrays in scala and Java using the ND4S/ND4J or Breeze libraries; Operations to "split" datasets across a Spark cluster by time or space or both. For example, a decade-long time-series of geo-variables can be split across time to enable parallel "speedups" of analysis by day, month, or season. Similarly, very high-resolution climate grids can be partitioned into spatial tiles for parallel operations across rows, columns, or blocks. In addition, using Spark's gateway into python, PySpark, one can utilize the entire ecosystem of numpy, scipy, etc. Finally, SciSpark Notebooks provide a modern eNotebook technology in which scala, python, or spark-sql codes are entered into cells in the Notebook and executed on the cluster, with results, plots, or graph visualizations displayed in "live widgets". We have exercised SciSpark by implementing three complex Use Cases: discovery and evolution of Mesoscale Convective Complexes (MCCs) in storms, yielding a graph of connected components; PDF Clustering of atmospheric state using parallel K-Means; and statistical "rollups" of geo-variables or model-to-obs. differences (i.e. mean, stddev, skewness, & kurtosis) by day, month, season, year, and multi-year. Geo-variables are ingested and split across the cluster using methods on the sciSparkContext object including netCDFVariables() for spatial decomposition and wholeNetCDFVariables() for time-series. The presentation will cover the architecture of SciSpark, the design of the scientific RDD (sRDD) data structures for N-dim. arrays, results from the three science Use Cases, example Notebooks, lessons learned from the algorithm implementations, and parallel performance metrics.

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.

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.

Automated problem scheduling and reduction of synchronization delay effects

NASA Technical Reports Server (NTRS)

Saltz, Joel H.

1987-01-01

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs.

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

TopoMS: Comprehensive topological exploration for molecular and condensed-matter systems.

PubMed

Bhatia, Harsh; Gyulassy, Attila G; Lordi, Vincenzo; Pask, John E; Pascucci, Valerio; Bremer, Peer-Timo

2018-06-15

We introduce TopoMS, a computational tool enabling detailed topological analysis of molecular and condensed-matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared-memory parallel approach, TopoMS provides scalable, numerically robust, and topologically consistent analysis. TopoMS can be used as a command-line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph. This paper presents algorithmic details of TopoMS and compares it with state-of-the-art tools: Bader charge analysis v1.0 (Arnaldsson et al., 01/11/17) and molecular graph extraction using Critic2 (Otero-de-la-Roza et al., Comput. Phys. Commun. 2014, 185, 1007). TopoMS not only combines the functionality of these individual codes but also demonstrates up to 4× performance gain on a standard laptop, faster convergence to fine-grid solution, robustness against lattice bias, and topological consistency. TopoMS is released publicly under BSD License. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Reliability models for dataflow computer systems

NASA Technical Reports Server (NTRS)

Kavi, K. M.; Buckles, B. P.

1985-01-01

The demands for concurrent operation within a computer system and the representation of parallelism in programming languages have yielded a new form of program representation known as data flow (DENN 74, DENN 75, TREL 82a). A new model based on data flow principles for parallel computations and parallel computer systems is presented. Necessary conditions for liveness and deadlock freeness in data flow graphs are derived. The data flow graph is used as a model to represent asynchronous concurrent computer architectures including data flow computers.

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

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.

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.

Using hybridization networks to retrace the evolution of Indo-European languages.

PubMed

Willems, Matthieu; Lord, Etienne; Laforest, Louise; Labelle, Gilbert; Lapointe, François-Joseph; Di Sciullo, Anna Maria; Makarenkov, Vladimir

2016-09-06

Curious parallels between the processes of species and language evolution have been observed by many researchers. Retracing the evolution of Indo-European (IE) languages remains one of the most intriguing intellectual challenges in historical linguistics. Most of the IE language studies use the traditional phylogenetic tree model to represent the evolution of natural languages, thus not taking into account reticulate evolutionary events, such as language hybridization and word borrowing which can be associated with species hybridization and horizontal gene transfer, respectively. More recently, implicit evolutionary networks, such as split graphs and minimal lateral networks, have been used to account for reticulate evolution in linguistics. Striking parallels existing between the evolution of species and natural languages allowed us to apply three computational biology methods for reconstruction of phylogenetic networks to model the evolution of IE languages. We show how the transfer of methods between the two disciplines can be achieved, making necessary methodological adaptations. Considering basic vocabulary data from the well-known Dyen's lexical database, which contains word forms in 84 IE languages for the meanings of a 200-meaning Swadesh list, we adapt a recently developed computational biology algorithm for building explicit hybridization networks to study the evolution of IE languages and compare our findings to the results provided by the split graph and galled network methods. We conclude that explicit phylogenetic networks can be successfully used to identify donors and recipients of lexical material as well as the degree of influence of each donor language on the corresponding recipient languages. We show that our algorithm is well suited to detect reticulate relationships among languages, and present some historical and linguistic justification for the results obtained. Our findings could be further refined if relevant syntactic, phonological and morphological data could be analyzed along with the available lexical data.

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.

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…

Student Reasoning about Graphs in Different Contexts

ERIC Educational Resources Information Center

Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

2016-01-01

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…

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.

A novel line segment detection algorithm based on graph search

NASA Astrophysics Data System (ADS)

Zhao, Hong-dan; Liu, Guo-ying; Song, Xu

2018-02-01

To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).

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.

Searching social networks for subgraph patterns

NASA Astrophysics Data System (ADS)

Ogaard, Kirk; Kase, Sue; Roy, Heather; Nagi, Rakesh; Sambhoos, Kedar; Sudit, Moises

2013-06-01

Software tools for Social Network Analysis (SNA) are being developed which support various types of analysis of social networks extracted from social media websites (e.g., Twitter). Once extracted and stored in a database such social networks are amenable to analysis by SNA software. This data analysis often involves searching for occurrences of various subgraph patterns (i.e., graphical representations of entities and relationships). The authors have developed the Graph Matching Toolkit (GMT) which provides an intuitive Graphical User Interface (GUI) for a heuristic graph matching algorithm called the Truncated Search Tree (TruST) algorithm. GMT is a visual interface for graph matching algorithms processing large social networks. GMT enables an analyst to draw a subgraph pattern by using a mouse to select categories and labels for nodes and links from drop-down menus. GMT then executes the TruST algorithm to find the top five occurrences of the subgraph pattern within the social network stored in the database. GMT was tested using a simulated counter-insurgency dataset consisting of cellular phone communications within a populated area of operations in Iraq. The results indicated GMT (when executing the TruST graph matching algorithm) is a time-efficient approach to searching large social networks. GMT's visual interface to a graph matching algorithm enables intelligence analysts to quickly analyze and summarize the large amounts of data necessary to produce actionable intelligence.

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.

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

PubMed Central

Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

2015-01-01

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

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.

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

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.

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.

Comparison of University Students' Understanding of Graphs in Different Contexts

ERIC Educational Resources Information Center

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-01-01

This study investigates university students' understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was…

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.

Distributed-Memory Breadth-First Search on Massive Graphs

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

Buluc, Aydin; Beamer, Scott; Madduri, Kamesh

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.

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.

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

Distributed memory parallel Markov random fields using graph partitioning

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

Heinemann, C.; Perciano, T.; Ushizima, D.

Markov random fields (MRF) based algorithms have attracted a large amount of interest in image analysis due to their ability to exploit contextual information about data. Image data generated by experimental facilities, though, continues to grow larger and more complex, making it more difficult to analyze in a reasonable amount of time. Applying image processing algorithms to large datasets requires alternative approaches to circumvent performance problems. Aiming to provide scientists with a new tool to recover valuable information from such datasets, we developed a general purpose distributed memory parallel MRF-based image analysis framework (MPI-PMRF). MPI-PMRF overcomes performance and memory limitationsmore » by distributing data and computations across processors. The proposed approach was successfully tested with synthetic and experimental datasets. Additionally, the performance of the MPI-PMRF framework is analyzed through a detailed scalability study. We show that a performance increase is obtained while maintaining an accuracy of the segmentation results higher than 98%. The contributions of this paper are: (a) development of a distributed memory MRF framework; (b) measurement of the performance increase of the proposed approach; (c) verification of segmentation accuracy in both synthetic and experimental, real-world datasets« less

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.

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.

Parsing Flowcharts and Series-Parallel Graphs

DTIC Science & Technology

1978-11-01

descriptions of the graph. This possible multiplicity is undesirable in most practical applications, a fact that makes parti%:ularly useful reduction...to parse TT networks, some of the features that make this parsing method useful in other cases are more natually introduced in the context of this...as Figure 4.5 shows. This multiplicity is due to the associativity of consecutive Two Terminal Series and Two Terminal Parallel compositions. In spite

Pruning Rogue Taxa Improves Phylogenetic Accuracy: An Efficient Algorithm and Webservice

PubMed Central

Aberer, Andre J.; Krompass, Denis; Stamatakis, Alexandros

2013-01-01

Abstract The presence of rogue taxa (rogues) in a set of trees can frequently have a negative impact on the results of a bootstrap analysis (e.g., the overall support in consensus trees). We introduce an efficient graph-based algorithm for rogue taxon identification as well as an interactive webservice implementing this algorithm. Compared with our previous method, the new algorithm is up to 4 orders of magnitude faster, while returning qualitatively identical results. Because of this significant improvement in scalability, the new algorithm can now identify substantially more complex and compute-intensive rogue taxon constellations. On a large and diverse collection of real-world data sets, we show that our method yields better supported reduced/pruned consensus trees than any competing rogue taxon identification method. Using the parallel version of our open-source code, we successfully identified rogue taxa in a set of 100 trees with 116 334 taxa each. For simulated data sets, we show that when removing/pruning rogue taxa with our method from a tree set, we consistently obtain bootstrap consensus trees as well as maximum-likelihood trees that are topologically closer to the respective true trees. PMID:22962004

Pruning rogue taxa improves phylogenetic accuracy: an efficient algorithm and webservice.

PubMed

Aberer, Andre J; Krompass, Denis; Stamatakis, Alexandros

2013-01-01

The presence of rogue taxa (rogues) in a set of trees can frequently have a negative impact on the results of a bootstrap analysis (e.g., the overall support in consensus trees). We introduce an efficient graph-based algorithm for rogue taxon identification as well as an interactive webservice implementing this algorithm. Compared with our previous method, the new algorithm is up to 4 orders of magnitude faster, while returning qualitatively identical results. Because of this significant improvement in scalability, the new algorithm can now identify substantially more complex and compute-intensive rogue taxon constellations. On a large and diverse collection of real-world data sets, we show that our method yields better supported reduced/pruned consensus trees than any competing rogue taxon identification method. Using the parallel version of our open-source code, we successfully identified rogue taxa in a set of 100 trees with 116 334 taxa each. For simulated data sets, we show that when removing/pruning rogue taxa with our method from a tree set, we consistently obtain bootstrap consensus trees as well as maximum-likelihood trees that are topologically closer to the respective true trees.

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

Memoryless cooperative graph search based on the simulated annealing algorithm

NASA Astrophysics Data System (ADS)

Hou, Jian; Yan, Gang-Feng; Fan, Zhen

2011-04-01

We have studied the problem of reaching a globally optimal segment for a graph-like environment with a single or a group of autonomous mobile agents. Firstly, two efficient simulated-annealing-like algorithms are given for a single agent to solve the problem in a partially known environment and an unknown environment, respectively. It shows that under both proposed control strategies, the agent will eventually converge to a globally optimal segment with probability 1. Secondly, we use multi-agent searching to simultaneously reduce the computation complexity and accelerate convergence based on the algorithms we have given for a single agent. By exploiting graph partition, a gossip-consensus method based scheme is presented to update the key parameter—radius of the graph, ensuring that the agents spend much less time finding a globally optimal segment.

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

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.

An Improved Heuristic Method for Subgraph Isomorphism Problem

NASA Astrophysics Data System (ADS)

Xiang, Yingzhuo; Han, Jiesi; Xu, Haijiang; Guo, Xin

2017-09-01

This paper focus on the subgraph isomorphism (SI) problem. We present an improved genetic algorithm, a heuristic method to search the optimal solution. The contribution of this paper is that we design a dedicated crossover algorithm and a new fitness function to measure the evolution process. Experiments show our improved genetic algorithm performs better than other heuristic methods. For a large graph, such as a subgraph of 40 nodes, our algorithm outperforms the traditional tree search algorithms. We find that the performance of our improved genetic algorithm does not decrease as the number of nodes in prototype graphs.

smoothG

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

Barker, Andrew T.; Gelever, Stephan A.; Lee, Chak S.

2017-12-12

smoothG is a collection of parallel C++ classes/functions that algebraically constructs reduced models of different resolutions from a given high-fidelity graph model. In addition, smoothG also provides efficient linear solvers for the reduced models. Other than pure graph problem, the software finds its application in subsurface flow and power grid simulations in which graph Laplacians are found

Comparison of Student Understanding of Line Graph Slope in Physics and Mathematics

ERIC Educational Resources Information Center

Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana

2012-01-01

This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

A Novel Coarsening Method for Scalable and Efficient Mesh Generation

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

Yoo, A; Hysom, D; Gunney, B

2010-12-02

In this paper, we propose a novel mesh coarsening method called brick coarsening method. The proposed method can be used in conjunction with any graph partitioners and scales to very large meshes. This method reduces problem space by decomposing the original mesh into fixed-size blocks of nodes called bricks, layered in a similar way to conventional brick laying, and then assigning each node of the original mesh to appropriate brick. Our experiments indicate that the proposed method scales to very large meshes while allowing simple RCB partitioner to produce higher-quality partitions with significantly less edge cuts. Our results further indicatemore » that the proposed brick-coarsening method allows more complicated partitioners like PT-Scotch to scale to very large problem size while still maintaining good partitioning performance with relatively good edge-cut metric. Graph partitioning is an important problem that has many scientific and engineering applications in such areas as VLSI design, scientific computing, and resource management. Given a graph G = (V,E), where V is the set of vertices and E is the set of edges, (k-way) graph partitioning problem is to partition the vertices of the graph (V) into k disjoint groups such that each group contains roughly equal number of vertices and the number of edges connecting vertices in different groups is minimized. Graph partitioning plays a key role in large scientific computing, especially in mesh-based computations, as it is used as a tool to minimize the volume of communication and to ensure well-balanced load across computing nodes. The impact of graph partitioning on the reduction of communication can be easily seen, for example, in different iterative methods to solve a sparse system of linear equation. Here, a graph partitioning technique is applied to the matrix, which is basically a graph in which each edge is a non-zero entry in the matrix, to allocate groups of vertices to processors in such a way that many of matrix-vector multiplication can be performed locally on each processor and hence to minimize communication. Furthermore, a good graph partitioning scheme ensures the equal amount of computation performed on each processor. Graph partitioning is a well known NP-complete problem, and thus the most commonly used graph partitioning algorithms employ some forms of heuristics. These algorithms vary in terms of their complexity, partition generation time, and the quality of partitions, and they tend to trade off these factors. A significant challenge we are currently facing at the Lawrence Livermore National Laboratory is how to partition very large meshes on massive-size distributed memory machines like IBM BlueGene/P, where scalability becomes a big issue. For example, we have found that the ParMetis, a very popular graph partitioning tool, can only scale to 16K processors. An ideal graph partitioning method on such an environment should be fast and scale to very large meshes, while producing high quality partitions. This is an extremely challenging task, as to scale to that level, the partitioning algorithm should be simple and be able to produce partitions that minimize inter-processor communications and balance the load imposed on the processors. Our goals in this work are two-fold: (1) To develop a new scalable graph partitioning method with good load balancing and communication reduction capability. (2) To study the performance of the proposed partitioning method on very large parallel machines using actual data sets and compare the performance to that of existing methods. The proposed method achieves the desired scalability by reducing the mesh size. For this, it coarsens an input mesh into a smaller size mesh by coalescing the vertices and edges of the original mesh into a set of mega-vertices and mega-edges. A new coarsening method called brick algorithm is developed in this research. In the brick algorithm, the zones in a given mesh are first grouped into fixed size blocks called bricks. These brick are then laid in a way similar to conventional brick laying technique, which reduces the number of neighboring blocks each block needs to communicate. Contributions of this research are as follows: (1) We have developed a novel method that scales to a really large problem size while producing high quality mesh partitions; (2) We measured the performance and scalability of the proposed method on a machine of massive size using a set of actual large complex data sets, where we have scaled to a mesh with 110 million zones using our method. To the best of our knowledge, this is the largest complex mesh that a partitioning method is successfully applied to; and (3) We have shown that proposed method can reduce the number of edge cuts by as much as 65%.« less

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

Ontology-based topic clustering for online discussion data

NASA Astrophysics Data System (ADS)

Wang, Yongheng; Cao, Kening; Zhang, Xiaoming

2013-03-01

With the rapid development of online communities, mining and extracting quality knowledge from online discussions becomes very important for the industrial and marketing sector, as well as for e-commerce applications and government. Most of the existing techniques model a discussion as a social network of users represented by a user-based graph without considering the content of the discussion. In this paper we propose a new multilayered mode to analysis online discussions. The user-based and message-based representation is combined in this model. A novel frequent concept sets based clustering method is used to cluster the original online discussion network into topic space. Domain ontology is used to improve the clustering accuracy. Parallel methods are also used to make the algorithms scalable to very large data sets. Our experimental study shows that the model and algorithms are effective when analyzing large scale online discussion data.

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.

Rapid geodesic mapping of brain functional connectivity: implementation of a dedicated co-processor in a field-programmable gate array (FPGA) and application to resting state functional MRI.

PubMed

Minati, Ludovico; Cercignani, Mara; Chan, Dennis

2013-10-01

Graph theory-based analyses of brain network topology can be used to model the spatiotemporal correlations in neural activity detected through fMRI, and such approaches have wide-ranging potential, from detection of alterations in preclinical Alzheimer's disease through to command identification in brain-machine interfaces. However, due to prohibitive computational costs, graph-based analyses to date have principally focused on measuring connection density rather than mapping the topological architecture in full by exhaustive shortest-path determination. This paper outlines a solution to this problem through parallel implementation of Dijkstra's algorithm in programmable logic. The processor design is optimized for large, sparse graphs and provided in full as synthesizable VHDL code. An acceleration factor between 15 and 18 is obtained on a representative resting-state fMRI dataset, and maps of Euclidean path length reveal the anticipated heterogeneous cortical involvement in long-range integrative processing. These results enable high-resolution geodesic connectivity mapping for resting-state fMRI in patient populations and real-time geodesic mapping to support identification of imagined actions for fMRI-based brain-machine interfaces. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

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

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.

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

A local search for a graph clustering problem

NASA Astrophysics Data System (ADS)

Navrotskaya, Anna; Il'ev, Victor

2016-10-01

In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.

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.

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.

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

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.

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.

Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data.

PubMed

Gallant, Andrew; Leiserson, Mark D M; Kachalov, Maxim; Cowen, Lenore J; Hescott, Benjamin J

2013-01-18

New technology has resulted in high-throughput screens for pairwise genetic interactions in yeast and other model organisms. For each pair in a collection of non-essential genes, an epistasis score is obtained, representing how much sicker (or healthier) the double-knockout organism will be compared to what would be expected from the sickness of the component single knockouts. Recent algorithmic work has identified graph-theoretic patterns in this data that can indicate functional modules, and even sets of genes that may occur in compensatory pathways, such as a BPM-type schema first introduced by Kelley and Ideker. However, to date, any algorithms for finding such patterns in the data were implemented internally, with no software being made publically available. Genecentric is a new package that implements a parallelized version of the Leiserson et al. algorithm (J Comput Biol 18:1399-1409, 2011) for generating generalized BPMs from high-throughput genetic interaction data. Given a matrix of weighted epistasis values for a set of double knock-outs, Genecentric returns a list of generalized BPMs that may represent compensatory pathways. Genecentric also has an extension, GenecentricGO, to query FuncAssociate (Bioinformatics 25:3043-3044, 2009) to retrieve GO enrichment statistics on generated BPMs. Python is the only dependency, and our web site provides working examples and documentation. We find that Genecentric can be used to find coherent functional and perhaps compensatory gene sets from high throughput genetic interaction data. Genecentric is made freely available for download under the GPLv2 from http://bcb.cs.tufts.edu/genecentric.

Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data

PubMed Central

2013-01-01

Background New technology has resulted in high-throughput screens for pairwise genetic interactions in yeast and other model organisms. For each pair in a collection of non-essential genes, an epistasis score is obtained, representing how much sicker (or healthier) the double-knockout organism will be compared to what would be expected from the sickness of the component single knockouts. Recent algorithmic work has identified graph-theoretic patterns in this data that can indicate functional modules, and even sets of genes that may occur in compensatory pathways, such as a BPM-type schema first introduced by Kelley and Ideker. However, to date, any algorithms for finding such patterns in the data were implemented internally, with no software being made publically available. Results Genecentric is a new package that implements a parallelized version of the Leiserson et al. algorithm (J Comput Biol 18:1399-1409, 2011) for generating generalized BPMs from high-throughput genetic interaction data. Given a matrix of weighted epistasis values for a set of double knock-outs, Genecentric returns a list of generalized BPMs that may represent compensatory pathways. Genecentric also has an extension, GenecentricGO, to query FuncAssociate (Bioinformatics 25:3043-3044, 2009) to retrieve GO enrichment statistics on generated BPMs. Python is the only dependency, and our web site provides working examples and documentation. Conclusion We find that Genecentric can be used to find coherent functional and perhaps compensatory gene sets from high throughput genetic interaction data. Genecentric is made freely available for download under the GPLv2 from http://bcb.cs.tufts.edu/genecentric. PMID:23331614

Computational Particle Dynamic Simulations on Multicore Processors (CPDMu) Final Report Phase I

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

Schmalz, Mark S

2011-07-24

Statement of Problem - Department of Energy has many legacy codes for simulation of computational particle dynamics and computational fluid dynamics applications that are designed to run on sequential processors and are not easily parallelized. Emerging high-performance computing architectures employ massively parallel multicore architectures (e.g., graphics processing units) to increase throughput. Parallelization of legacy simulation codes is a high priority, to achieve compatibility, efficiency, accuracy, and extensibility. General Statement of Solution - A legacy simulation application designed for implementation on mainly-sequential processors has been represented as a graph G. Mathematical transformations, applied to G, produce a graph representation {und G}more » for a high-performance architecture. Key computational and data movement kernels of the application were analyzed/optimized for parallel execution using the mapping G {yields} {und G}, which can be performed semi-automatically. This approach is widely applicable to many types of high-performance computing systems, such as graphics processing units or clusters comprised of nodes that contain one or more such units. Phase I Accomplishments - Phase I research decomposed/profiled computational particle dynamics simulation code for rocket fuel combustion into low and high computational cost regions (respectively, mainly sequential and mainly parallel kernels), with analysis of space and time complexity. Using the research team's expertise in algorithm-to-architecture mappings, the high-cost kernels were transformed, parallelized, and implemented on Nvidia Fermi GPUs. Measured speedups (GPU with respect to single-core CPU) were approximately 20-32X for realistic model parameters, without final optimization. Error analysis showed no loss of computational accuracy. Commercial Applications and Other Benefits - The proposed research will constitute a breakthrough in solution of problems related to efficient parallel computation of particle and fluid dynamics simulations. These problems occur throughout DOE, military and commercial sectors: the potential payoff is high. We plan to license or sell the solution to contractors for military and domestic applications such as disaster simulation (aerodynamic and hydrodynamic), Government agencies (hydrological and environmental simulations), and medical applications (e.g., in tomographic image reconstruction). Keywords - High-performance Computing, Graphic Processing Unit, Fluid/Particle Simulation. Summary for Members of Congress - Department of Energy has many simulation codes that must compute faster, to be effective. The Phase I research parallelized particle/fluid simulations for rocket combustion, for high-performance computing systems.« less

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

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

NASA Technical Reports Server (NTRS)

Long, Jason D.; Colombano, Silvano P.; Haith, Gary L.; Stassinopoulos, Dimitris

2000-01-01

Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.

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.

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

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

SciSpark: Highly Interactive and Scalable Model Evaluation and Climate Metrics

NASA Astrophysics Data System (ADS)

Wilson, B. D.; Mattmann, C. A.; Waliser, D. E.; Kim, J.; Loikith, P.; Lee, H.; McGibbney, L. J.; Whitehall, K. D.

2014-12-01

Remote sensing data and climate model output are multi-dimensional arrays of massive sizes locked away in heterogeneous file formats (HDF5/4, NetCDF 3/4) and metadata models (HDF-EOS, CF) making it difficult to perform multi-stage, iterative science processing since each stage requires writing and reading data to and from disk. We are developing a lightning fast Big Data technology called SciSpark based on ApacheTM Spark. Spark implements the map-reduce paradigm for parallel computing on a cluster, but emphasizes in-memory computation, "spilling" to disk only as needed, and so outperforms the disk-based ApacheTM Hadoop by 100x in memory and by 10x on disk, and makes iterative algorithms feasible. SciSpark will enable scalable model evaluation by executing large-scale comparisons of A-Train satellite observations to model grids on a cluster of 100 to 1000 compute nodes. This 2nd generation capability for NASA's Regional Climate Model Evaluation System (RCMES) will compute simple climate metrics at interactive speeds, and extend to quite sophisticated iterative algorithms such as machine-learning (ML) based clustering of temperature PDFs, and even graph-based algorithms for searching for Mesocale Convective Complexes. The goals of SciSpark are to: (1) Decrease the time to compute comparison statistics and plots from minutes to seconds; (2) Allow for interactive exploration of time-series properties over seasons and years; (3) Decrease the time for satellite data ingestion into RCMES to hours; (4) Allow for Level-2 comparisons with higher-order statistics or PDF's in minutes to hours; and (5) Move RCMES into a near real time decision-making platform. We will report on: the architecture and design of SciSpark, our efforts to integrate climate science algorithms in Python and Scala, parallel ingest and partitioning (sharding) of A-Train satellite observations from HDF files and model grids from netCDF files, first parallel runs to compute comparison statistics and PDF's, and first metrics quantifying parallel speedups and memory & disk usage.

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

EvoGraph: On-The-Fly Efficient Mining of Evolving Graphs on GPU

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

Sengupta, Dipanjan; Song, Shuaiwen

With the prevalence of the World Wide Web and social networks, there has been a growing interest in high performance analytics for constantly-evolving dynamic graphs. Modern GPUs provide massive AQ1 amount of parallelism for efficient graph processing, but the challenges remain due to their lack of support for the near real-time streaming nature of dynamic graphs. Specifically, due to the current high volume and velocity of graph data combined with the complexity of user queries, traditional processing methods by first storing the updates and then repeatedly running static graph analytics on a sequence of versions or snapshots are deemed undesirablemore » and computational infeasible on GPU. We present EvoGraph, a highly efficient and scalable GPU- based dynamic graph analytics framework.« less

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.

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…

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

Strout, Michelle

Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programsmore » through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.« less

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

Ant colony optimization for solving university facility layout problem

NASA Astrophysics Data System (ADS)

Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

2013-04-01

Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

A large-grain mapping approach for multiprocessor systems through data flow model. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kim, Hwa-Soo

1991-01-01

A large-grain level mapping method is presented of numerical oriented applications onto multiprocessor systems. The method is based on the large-grain data flow representation of the input application and it assumes a general interconnection topology of the multiprocessor system. The large-grain data flow model was used because such representation best exhibits inherited parallelism in many important applications, e.g., CFD models based on partial differential equations can be presented in large-grain data flow format, very effectively. A generalized interconnection topology of the multiprocessor architecture is considered, including such architectural issues as interprocessor communication cost, with the aim to identify the 'best matching' between the application and the multiprocessor structure. The objective is to minimize the total execution time of the input algorithm running on the target system. The mapping strategy consists of the following: (1) large-grain data flow graph generation from the input application using compilation techniques; (2) data flow graph partitioning into basic computation blocks; and (3) physical mapping onto the target multiprocessor using a priority allocation scheme for the computation blocks.

A quantum physical design flow using ILP and graph drawing

NASA Astrophysics Data System (ADS)

Yazdani, Maryam; Saheb Zamani, Morteza; Sedighi, Mehdi

2013-10-01

Implementing large-scale quantum circuits is one of the challenges of quantum computing. One of the central challenges of accurately modeling the architecture of these circuits is to schedule a quantum application and generate the layout while taking into account the cost of communications and classical resources as well as the maximum exploitable parallelism. In this paper, we present and evaluate a design flow for arbitrary quantum circuits in ion trap technology. Our design flow consists of two parts. First, a scheduler takes a description of a circuit and finds the best order for the execution of its quantum gates using integer linear programming regarding the classical resources (qubits) and instruction dependencies. Then a layout generator receives the schedule produced by the scheduler and generates a layout for this circuit using a graph-drawing algorithm. Our experimental results show that the proposed flow decreases the average latency of quantum circuits by about 11 % for a set of attempted benchmarks and by about 9 % for another set of benchmarks compared with the best in literature.

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

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.

Disk-based k-mer counting on a PC

PubMed Central

2013-01-01

Background The k-mer counting problem, which is to build the histogram of occurrences of every k-symbol long substring in a given text, is important for many bioinformatics applications. They include developing de Bruijn graph genome assemblers, fast multiple sequence alignment and repeat detection. Results We propose a simple, yet efficient, parallel disk-based algorithm for counting k-mers. Experiments show that it usually offers the fastest solution to the considered problem, while demanding a relatively small amount of memory. In particular, it is capable of counting the statistics for short-read human genome data, in input gzipped FASTQ file, in less than 40 minutes on a PC with 16 GB of RAM and 6 CPU cores, and for long-read human genome data in less than 70 minutes. On a more powerful machine, using 32 GB of RAM and 32 CPU cores, the tasks are accomplished in less than half the time. No other algorithm for most tested settings of this problem and mammalian-size data can accomplish this task in comparable time. Our solution also belongs to memory-frugal ones; most competitive algorithms cannot efficiently work on a PC with 16 GB of memory for such massive data. Conclusions By making use of cheap disk space and exploiting CPU and I/O parallelism we propose a very competitive k-mer counting procedure, called KMC. Our results suggest that judicious resource management may allow to solve at least some bioinformatics problems with massive data on a commodity personal computer. PMID:23679007

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.

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.

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

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.

Graph cuts via l1 norm minimization.

PubMed

Bhusnurmath, Arvind; Taylor, Camillo J

2008-10-01

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

Student reasoning about graphs in different contexts

NASA Astrophysics Data System (ADS)

Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

2016-06-01

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students' main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students' answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

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.

Multi-INT Complex Event Processing using Approximate, Incremental Graph Pattern Search

DTIC Science & Technology

2012-06-01

graph pattern search and SPARQL queries . Total execution time for 10 executions each of 5 random pattern searches in synthetic data sets...01/11 1000 10000 100000 RDF triples Time (secs) 10 20 Graph pattern algorithm SPARQL queries Initial Performance Comparisons 09/18/11 2011 Thrust Area

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…

Random sequential renormalization and agglomerative percolation in networks: application to Erdös-Rényi and scale-free graphs.

PubMed

Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-12-01

We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song et al., Nature (London) 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi et al. [Phys. Rev. Lett. 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering "supernodes" as clusters) are much easier to study using the fast Newman-Ziff algorithm for percolation, allowing us to obtain very high statistics.

Real-time optical flow estimation on a GPU for a skied-steered mobile robot

NASA Astrophysics Data System (ADS)

Kniaz, V. V.

2016-04-01

Accurate egomotion estimation is required for mobile robot navigation. Often the egomotion is estimated using optical flow algorithms. For an accurate estimation of optical flow most of modern algorithms require high memory resources and processor speed. However simple single-board computers that control the motion of the robot usually do not provide such resources. On the other hand, most of modern single-board computers are equipped with an embedded GPU that could be used in parallel with a CPU to improve the performance of the optical flow estimation algorithm. This paper presents a new Z-flow algorithm for efficient computation of an optical flow using an embedded GPU. The algorithm is based on the phase correlation optical flow estimation and provide a real-time performance on a low cost embedded GPU. The layered optical flow model is used. Layer segmentation is performed using graph-cut algorithm with a time derivative based energy function. Such approach makes the algorithm both fast and robust in low light and low texture conditions. The algorithm implementation for a Raspberry Pi Model B computer is discussed. For evaluation of the algorithm the computer was mounted on a Hercules mobile skied-steered robot equipped with a monocular camera. The evaluation was performed using a hardware-in-the-loop simulation and experiments with Hercules mobile robot. Also the algorithm was evaluated using KITTY Optical Flow 2015 dataset. The resulting endpoint error of the optical flow calculated with the developed algorithm was low enough for navigation of the robot along the desired trajectory.

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.

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.

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

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

Xi-cam: Flexible High Throughput Data Processing for GISAXS

NASA Astrophysics Data System (ADS)

Pandolfi, Ronald; Kumar, Dinesh; Venkatakrishnan, Singanallur; Sarje, Abinav; Krishnan, Hari; Pellouchoud, Lenson; Ren, Fang; Fournier, Amanda; Jiang, Zhang; Tassone, Christopher; Mehta, Apurva; Sethian, James; Hexemer, Alexander

With increasing capabilities and data demand for GISAXS beamlines, supporting software is under development to handle larger data rates, volumes, and processing needs. We aim to provide a flexible and extensible approach to GISAXS data treatment as a solution to these rising needs. Xi-cam is the CAMERA platform for data management, analysis, and visualization. The core of Xi-cam is an extensible plugin-based GUI platform which provides users an interactive interface to processing algorithms. Plugins are available for SAXS/GISAXS data and data series visualization, as well as forward modeling and simulation through HipGISAXS. With Xi-cam's advanced mode, data processing steps are designed as a graph-based workflow, which can be executed locally or remotely. Remote execution utilizes HPC or de-localized resources, allowing for effective reduction of high-throughput data. Xi-cam is open-source and cross-platform. The processing algorithms in Xi-cam include parallel cpu and gpu processing optimizations, also taking advantage of external processing packages such as pyFAI. Xi-cam is available for download online.

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

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

PubMed

Chakraborty, Shantanav; Novo, Leonardo; Ambainis, Andris; Omar, Yasser

2016-03-11

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e., graphs of n vertices where each edge exists with probability p, search by CTQW is almost surely optimal as long as p≥log^{3/2}(n)/n. Consequently, we show that quantum spatial search is in fact optimal for almost all graphs, meaning that the fraction of graphs of n vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely, to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

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.

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.

Graphics-Based Parallel Programming Tools

DTIC Science & Technology

1991-09-01

mean "beyond" (as in " paranormal "). emphasizing the fact that the editor supports the specification of not just single graphs, but entire graph...conflicting dependencies: all processes see the three steps in the same order and all interprocess communication happens within a step. 6 Not all abstract

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

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.

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

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.

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.

Fast parallel algorithm for slicing STL based on pipeline

NASA Astrophysics Data System (ADS)

Ma, Xulong; Lin, Feng; Yao, Bo

2016-05-01

In Additive Manufacturing field, the current researches of data processing mainly focus on a slicing process of large STL files or complicated CAD models. To improve the efficiency and reduce the slicing time, a parallel algorithm has great advantages. However, traditional algorithms can't make full use of multi-core CPU hardware resources. In the paper, a fast parallel algorithm is presented to speed up data processing. A pipeline mode is adopted to design the parallel algorithm. And the complexity of the pipeline algorithm is analyzed theoretically. To evaluate the performance of the new algorithm, effects of threads number and layers number are investigated by a serial of experiments. The experimental results show that the threads number and layers number are two remarkable factors to the speedup ratio. The tendency of speedup versus threads number reveals a positive relationship which greatly agrees with the Amdahl's law, and the tendency of speedup versus layers number also keeps a positive relationship agreeing with Gustafson's law. The new algorithm uses topological information to compute contours with a parallel method of speedup. Another parallel algorithm based on data parallel is used in experiments to show that pipeline parallel mode is more efficient. A case study at last shows a suspending performance of the new parallel algorithm. Compared with the serial slicing algorithm, the new pipeline parallel algorithm can make full use of the multi-core CPU hardware, accelerate the slicing process, and compared with the data parallel slicing algorithm, the new slicing algorithm in this paper adopts a pipeline parallel model, and a much higher speedup ratio and efficiency is achieved.

Graph-based linear scaling electronic structure theory.

PubMed

Niklasson, Anders M N; Mniszewski, Susan M; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Rubensson, Emanuel H; Djidjev, Hristo

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graph-based linear scaling electronic structure theory

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

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix

NASA Technical Reports Server (NTRS)

Shroff, Gautam

1989-01-01

A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.

Parallel algorithms for placement and routing in VLSI design. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Brouwer, Randall Jay

1991-01-01

The computational requirements for high quality synthesis, analysis, and verification of very large scale integration (VLSI) designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or parallel algorithms for the numerous design tasks to decrease the time required for solution. Two new parallel algorithms are proposed for two VLSI synthesis tasks, standard cell placement and global routing. The first algorithm, a parallel algorithm for global routing, uses hierarchical techniques to decompose the routing problem into independent routing subproblems that are solved in parallel. Results are then presented which compare the routing quality to the results of other published global routers and which evaluate the speedups attained. The second algorithm, a parallel algorithm for cell placement and global routing, hierarchically integrates a quadrisection placement algorithm, a bisection placement algorithm, and the previous global routing algorithm. Unique partitioning techniques are used to decompose the various stages of the algorithm into independent tasks which can be evaluated in parallel. Finally, results are presented which evaluate the various algorithm alternatives and compare the algorithm performance to other placement programs. Measurements are presented on the parallel speedups available.

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 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.

Multidimensional spectral load balancing

DOEpatents

Hendrickson, Bruce A.; Leland, Robert W.

1996-12-24

A method of and apparatus for graph partitioning involving the use of a plurality of eigenvectors of the Laplacian matrix of the graph of the problem for which load balancing is desired. The invention is particularly useful for optimizing parallel computer processing of a problem and for minimizing total pathway lengths of integrated circuits in the design stage.

Modifying the Test of Understanding Graphs in Kinematics

ERIC Educational Resources Information Center

Zavala, Genaro; Tejeda, Santa; Barniol, Pablo; Beichner, Robert J.

2017-01-01

In this article, we present several modifications to the Test of Understanding Graphs in Kinematics. The most significant changes are (i) the addition and removal of items to achieve parallelism in the objectives (dimensions) of the test, thus allowing comparisons of students' performance that were not possible with the original version, and (ii)…

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.

SciSpark: Highly Interactive and Scalable Model Evaluation and Climate Metrics

NASA Astrophysics Data System (ADS)

Wilson, B. D.; Palamuttam, R. S.; Mogrovejo, R. M.; Whitehall, K. D.; Mattmann, C. A.; Verma, R.; Waliser, D. E.; Lee, H.

2015-12-01

Remote sensing data and climate model output are multi-dimensional arrays of massive sizes locked away in heterogeneous file formats (HDF5/4, NetCDF 3/4) and metadata models (HDF-EOS, CF) making it difficult to perform multi-stage, iterative science processing since each stage requires writing and reading data to and from disk. We are developing a lightning fast Big Data technology called SciSpark based on ApacheTM Spark under a NASA AIST grant (PI Mattmann). Spark implements the map-reduce paradigm for parallel computing on a cluster, but emphasizes in-memory computation, "spilling" to disk only as needed, and so outperforms the disk-based ApacheTM Hadoop by 100x in memory and by 10x on disk. SciSpark will enable scalable model evaluation by executing large-scale comparisons of A-Train satellite observations to model grids on a cluster of 10 to 1000 compute nodes. This 2nd generation capability for NASA's Regional Climate Model Evaluation System (RCMES) will compute simple climate metrics at interactive speeds, and extend to quite sophisticated iterative algorithms such as machine-learning based clustering of temperature PDFs, and even graph-based algorithms for searching for Mesocale Convective Complexes. We have implemented a parallel data ingest capability in which the user specifies desired variables (arrays) as several time-sorted lists of URL's (i.e. using OPeNDAP model.nc?varname, or local files). The specified variables are partitioned by time/space and then each Spark node pulls its bundle of arrays into memory to begin a computation pipeline. We also investigated the performance of several N-dim. array libraries (scala breeze, java jblas & netlib-java, and ND4J). We are currently developing science codes using ND4J and studying memory behavior on the JVM. On the pyspark side, many of our science codes already use the numpy and SciPy ecosystems. The talk will cover: the architecture of SciSpark, the design of the scientific RDD (sRDD) data structure, our efforts to integrate climate science algorithms in Python and Scala, parallel ingest and partitioning of A-Train satellite observations from HDF files and model grids from netCDF files, first parallel runs to compute comparison statistics and PDF's, and first metrics quantifying parallel speedups and memory & disk usage.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

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.

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

CYBERWAR-2012/13: Siegel 2011 Predicted Cyberwar Via ACHILLES-HEEL DIGITS BEQS BEC ZERO-DIGIT BEC of/in ACHILLES-HEEL DIGITS Log-Law Algebraic-Inversion to ONLY BEQS BEC Digit-Physics U Barabasi Network/Graph-Physics BEQS BEC JAMMING Denial-of-Access(DOA) Attacks 2012-Instantiations

NASA Astrophysics Data System (ADS)

Huffmann, Master; Siegel, Edward Carl-Ludwig

2013-03-01

Newcomb-Benford(NeWBe)-Siegel log-law BEC Digit-Physics Network/Graph-Physics Barabasi et.al. evolving-``complex''-networks/graphs BEC JAMMING DOA attacks: Amazon(weekends: Microsoft I.E.-7/8(vs. Firefox): Memorial-day, Labor-day,...), MANY U.S.-Banks:WF,BoA,UB,UBS,...instantiations AGAIN militate for MANDATORY CONVERSION to PARALLEL ANALOG FAULT-TOLERANT but slow(er) SECURITY-ASSURANCE networks/graphs in parallel with faster ``sexy'' DIGITAL-Networks/graphs:``Cloud'', telecomm: n-G,..., because of common ACHILLES-HEEL VULNERABILITY: DIGITS!!! ``In fast-hare versus slow-tortoise race, Slow-But-Steady ALWAYS WINS!!!'' (Zeno). {Euler [#s(1732)] ∑- ∏()-Riemann[Monats. Akad. Berlin (1859)] ∑- ∏()- Kummer-Bernoulli (#s)}-Newcomb [Am.J.Math.4(1),39 (81) discovery of the QUANTUM!!!]-{Planck (01)]}-{Einstein (05)]-Poincar e [Calcul Probabilités,313(12)]-Weyl[Goett. Nach.(14); Math.Ann.77,313(16)]-(Bose (24)-Einstein(25)]-VS. -Fermi (27)-Dirac(27))-Menger [Dimensiontheorie(29)]-Benford [J.Am. Phil.Soc.78,115(38)]-Kac[Maths Stats.-Reason. (55)]- Raimi [Sci.Am.221,109(69)]-Jech-Hill [Proc.AMS,123,3,887(95)] log-function

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/

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

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.

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.

Optimal Quantum Spatial Search on Random Temporal Networks

NASA Astrophysics Data System (ADS)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

A class of parallel algorithms for computation of the manipulator inertia matrix

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

Parallel and parallel/pipeline algorithms for computation of the manipulator inertia matrix are presented. An algorithm based on composite rigid-body spatial inertia method, which provides better features for parallelization, is used for the computation of the inertia matrix. Two parallel algorithms are developed which achieve the time lower bound in computation. Also described is the mapping of these algorithms with topological variation on a two-dimensional processor array, with nearest-neighbor connection, and with cardinality variation on a linear processor array. An efficient parallel/pipeline algorithm for the linear array was also developed, but at significantly higher efficiency.

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.

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.

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

Introducing parallelism to histogramming functions for GEM systems

NASA Astrophysics Data System (ADS)

Krawczyk, Rafał D.; Czarski, Tomasz; Kolasinski, Piotr; Pozniak, Krzysztof T.; Linczuk, Maciej; Byszuk, Adrian; Chernyshova, Maryna; Juszczyk, Bartlomiej; Kasprowicz, Grzegorz; Wojenski, Andrzej; Zabolotny, Wojciech

2015-09-01

This article is an assessment of potential parallelization of histogramming algorithms in GEM detector system. Histogramming and preprocessing algorithms in MATLAB were analyzed with regard to adding parallelism. Preliminary implementation of parallel strip histogramming resulted in speedup. Analysis of algorithms parallelizability is presented. Overview of potential hardware and software support to implement parallel algorithm is discussed.

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.

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

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.

The development of a scalable parallel 3-D CFD algorithm for turbomachinery. M.S. Thesis Final Report

NASA Technical Reports Server (NTRS)

Luke, Edward Allen

1993-01-01

Two algorithms capable of computing a transonic 3-D inviscid flow field about rotating machines are considered for parallel implementation. During the study of these algorithms, a significant new method of measuring the performance of parallel algorithms is developed. The theory that supports this new method creates an empirical definition of scalable parallel algorithms that is used to produce quantifiable evidence that a scalable parallel application was developed. The implementation of the parallel application and an automated domain decomposition tool are also discussed.

P-HARP: A parallel dynamic spectral partitioner

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

Sohn, A.; Biswas, R.; Simon, H.D.

1997-05-01

Partitioning unstructured graphs is central to the parallel solution of problems in computational science and engineering. The authors have introduced earlier the sequential version of an inertial spectral partitioner called HARP which maintains the quality of recursive spectral bisection (RSB) while forming the partitions an order of magnitude faster than RSB. The serial HARP is known to be the fastest spectral partitioner to date, three to four times faster than similar partitioners on a variety of meshes. This paper presents a parallel version of HARP, called P-HARP. Two types of parallelism have been exploited: loop level parallelism and recursive parallelism.more » P-HARP has been implemented in MPI on the SGI/Cray T3E and the IBM SP2. Experimental results demonstrate that P-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.25 seconds on a 64-processor T3E. Experimental results further show that P-HARP can give nearly a 20-fold speedup on 64 processors. These results indicate that graph partitioning is no longer a major bottleneck that hinders the advancement of computational science and engineering for dynamically-changing real-world applications.« less

Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm

NASA Astrophysics Data System (ADS)

Backes, Werner; Wetzel, Susanne

In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multi-threaded algorithm is the first to provide an efficient, parallel implementation of the Schorr-Euchner algorithm for today’s multi-processor, multi-core computer architectures. Experiments with sparse and dense lattice bases show a speed-up factor of about 1.8 for the 2-thread and about factor 3.2 for the 4-thread version of our new parallel lattice basis reduction algorithm in comparison to the traditional non-parallel algorithm.

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

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.

High-Performance Psychometrics: The Parallel-E Parallel-M Algorithm for Generalized Latent Variable Models. Research Report. ETS RR-16-34

ERIC Educational Resources Information Center

von Davier, Matthias

2016-01-01

This report presents results on a parallel implementation of the expectation-maximization (EM) algorithm for multidimensional latent variable models. The developments presented here are based on code that parallelizes both the E step and the M step of the parallel-E parallel-M algorithm. Examples presented in this report include item response…

ProperCAD: A portable object-oriented parallel environment for VLSI CAD

NASA Technical Reports Server (NTRS)

Ramkumar, Balkrishna; Banerjee, Prithviraj

1993-01-01

Most parallel algorithms for VLSI CAD proposed to date have one important drawback: they work efficiently only on machines that they were designed for. As a result, algorithms designed to date are dependent on the architecture for which they are developed and do not port easily to other parallel architectures. A new project under way to address this problem is described. A Portable object-oriented parallel environment for CAD algorithms (ProperCAD) is being developed. The objectives of this research are (1) to develop new parallel algorithms that run in a portable object-oriented environment (CAD algorithms using a general purpose platform for portable parallel programming called CARM is being developed and a C++ environment that is truly object-oriented and specialized for CAD applications is also being developed); and (2) to design the parallel algorithms around a good sequential algorithm with a well-defined parallel-sequential interface (permitting the parallel algorithm to benefit from future developments in sequential algorithms). One CAD application that has been implemented as part of the ProperCAD project, flat VLSI circuit extraction, is described. The algorithm, its implementation, and its performance on a range of parallel machines are discussed in detail. It currently runs on an Encore Multimax, a Sequent Symmetry, Intel iPSC/2 and i860 hypercubes, a NCUBE 2 hypercube, and a network of Sun Sparc workstations. Performance data for other applications that were developed are provided: namely test pattern generation for sequential circuits, parallel logic synthesis, and standard cell placement.

Multitasking TORT under UNICOS: Parallel performance models and measurements

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

Barnett, A.; Azmy, Y.Y.

1999-09-27

The existing parallel algorithms in the TORT discrete ordinates code were updated to function in a UNICOS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead.

Multitasking TORT Under UNICOS: Parallel Performance Models and Measurements

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

Azmy, Y.Y.; Barnett, D.A.

1999-09-27

The existing parallel algorithms in the TORT discrete ordinates were updated to function in a UNI-COS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead.

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

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

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

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.

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

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.

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.

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.

Loops in hierarchical channel networks

NASA Astrophysics Data System (ADS)

Katifori, Eleni; Magnasco, Marcelo

2012-02-01

Nature provides us with many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated and natural graphs extracted from digitized images of dicotyledonous leaves and animal vasculature. We calculate various metrics on the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

Graph Matching: Relax at Your Own Risk.

PubMed

Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

2016-01-01

Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.

On transitions in the behaviour of tabu search algorithm TabuCol for graph colouring

NASA Astrophysics Data System (ADS)

Chalupa, D.

2018-01-01

Even though tabu search is one of the most popular metaheuristic search strategies, its understanding in terms of behavioural transitions and parameter tuning is still very limited. In this paper, we present a theoretical and experimental study of a popular tabu search algorithm TabuCol for graph colouring. We show that for some instances, there are sharp transitions in the behaviour of TabuCol, depending on the value of tabu tenure parameter. The location of this transition depends on graph structure and may also depend on its size. This is further supported by an experimental study of success rate profiles, which we define as an empirical measure of these transitions. We study the success rate profiles for a range of graph colouring instances, from 2-colouring of trees and forests to several instances from the DIMACS benchmark. These reveal that TabuCol may exhibit a spectrum of different behaviours ranging from simple transitions to highly complex probabilistic behaviour.

Constructing a Graph Database for Semantic Literature-Based Discovery.

PubMed

Hristovski, Dimitar; Kastrin, Andrej; Dinevski, Dejan; Rindflesch, Thomas C

2015-01-01

Literature-based discovery (LBD) generates discoveries, or hypotheses, by combining what is already known in the literature. Potential discoveries have the form of relations between biomedical concepts; for example, a drug may be determined to treat a disease other than the one for which it was intended. LBD views the knowledge in a domain as a network; a set of concepts along with the relations between them. As a starting point, we used SemMedDB, a database of semantic relations between biomedical concepts extracted with SemRep from Medline. SemMedDB is distributed as a MySQL relational database, which has some problems when dealing with network data. We transformed and uploaded SemMedDB into the Neo4j graph database, and implemented the basic LBD discovery algorithms with the Cypher query language. We conclude that storing the data needed for semantic LBD is more natural in a graph database. Also, implementing LBD discovery algorithms is conceptually simpler with a graph query language when compared with standard SQL.

MorphoGraphX: A platform for quantifying morphogenesis in 4D.

PubMed

Barbier de Reuille, Pierre; Routier-Kierzkowska, Anne-Lise; Kierzkowski, Daniel; Bassel, George W; Schüpbach, Thierry; Tauriello, Gerardo; Bajpai, Namrata; Strauss, Sören; Weber, Alain; Kiss, Annamaria; Burian, Agata; Hofhuis, Hugo; Sapala, Aleksandra; Lipowczan, Marcin; Heimlicher, Maria B; Robinson, Sarah; Bayer, Emmanuelle M; Basler, Konrad; Koumoutsakos, Petros; Roeder, Adrienne H K; Aegerter-Wilmsen, Tinri; Nakayama, Naomi; Tsiantis, Miltos; Hay, Angela; Kwiatkowska, Dorota; Xenarios, Ioannis; Kuhlemeier, Cris; Smith, Richard S

2015-05-06

Morphogenesis emerges from complex multiscale interactions between genetic and mechanical processes. To understand these processes, the evolution of cell shape, proliferation and gene expression must be quantified. This quantification is usually performed either in full 3D, which is computationally expensive and technically challenging, or on 2D planar projections, which introduces geometrical artifacts on highly curved organs. Here we present MorphoGraphX ( www.MorphoGraphX.org), a software that bridges this gap by working directly with curved surface images extracted from 3D data. In addition to traditional 3D image analysis, we have developed algorithms to operate on curved surfaces, such as cell segmentation, lineage tracking and fluorescence signal quantification. The software's modular design makes it easy to include existing libraries, or to implement new algorithms. Cell geometries extracted with MorphoGraphX can be exported and used as templates for simulation models, providing a powerful platform to investigate the interactions between shape, genes and growth.

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.

Tennis Rackets and the Parallel Axis Theorem

ERIC Educational Resources Information Center

Christie, Derek

2014-01-01

This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.

Aligning Biomolecular Networks Using Modular Graph Kernels

NASA Astrophysics Data System (ADS)

Towfic, Fadi; Greenlee, M. Heather West; Honavar, Vasant

Comparative analysis of biomolecular networks constructed using measurements from different conditions, tissues, and organisms offer a powerful approach to understanding the structure, function, dynamics, and evolution of complex biological systems. We explore a class of algorithms for aligning large biomolecular networks by breaking down such networks into subgraphs and computing the alignment of the networks based on the alignment of their subgraphs. The resulting subnetworks are compared using graph kernels as scoring functions. We provide implementations of the resulting algorithms as part of BiNA, an open source biomolecular network alignment toolkit. Our experiments using Drosophila melanogaster, Saccharomyces cerevisiae, Mus musculus and Homo sapiens protein-protein interaction networks extracted from the DIP repository of protein-protein interaction data demonstrate that the performance of the proposed algorithms (as measured by % GO term enrichment of subnetworks identified by the alignment) is competitive with some of the state-of-the-art algorithms for pair-wise alignment of large protein-protein interaction networks. Our results also show that the inter-species similarity scores computed based on graph kernels can be used to cluster the species into a species tree that is consistent with the known phylogenetic relationships among the species.

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.

Parallel consistent labeling algorithms

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

Samal, A.; Henderson, T.

Mackworth and Freuder have analyzed the time complexity of several constraint satisfaction algorithms. Mohr and Henderson have given new algorithms, AC-4 and PC-3, for arc and path consistency, respectively, and have shown that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms. In this paper, they give parallel algorithms for solving node and arc consistency. They show that any parallel algorithm for enforcing arc consistency in the worst case must have O(na) sequential steps, where n is number of nodes, and a is the number of labels per node.more » They give several parallel algorithms to do arc consistency. It is also shown that they all have optimal time complexity. The results of running the parallel algorithms on a BBN Butterfly multiprocessor are also presented.« less

chemf: A purely functional chemistry toolkit.

PubMed

Höck, Stefan; Riedl, Rainer

2012-12-20

Although programming in a type-safe and referentially transparent style offers several advantages over working with mutable data structures and side effects, this style of programming has not seen much use in chemistry-related software. Since functional programming languages were designed with referential transparency in mind, these languages offer a lot of support when writing immutable data structures and side-effects free code. We therefore started implementing our own toolkit based on the above programming paradigms in a modern, versatile programming language. We present our initial results with functional programming in chemistry by first describing an immutable data structure for molecular graphs together with a couple of simple algorithms to calculate basic molecular properties before writing a complete SMILES parser in accordance with the OpenSMILES specification. Along the way we show how to deal with input validation, error handling, bulk operations, and parallelization in a purely functional way. At the end we also analyze and improve our algorithms and data structures in terms of performance and compare it to existing toolkits both object-oriented and purely functional. All code was written in Scala, a modern multi-paradigm programming language with a strong support for functional programming and a highly sophisticated type system. We have successfully made the first important steps towards a purely functional chemistry toolkit. The data structures and algorithms presented in this article perform well while at the same time they can be safely used in parallelized applications, such as computer aided drug design experiments, without further adjustments. This stands in contrast to existing object-oriented toolkits where thread safety of data structures and algorithms is a deliberate design decision that can be hard to implement. Finally, the level of type-safety achieved by Scala highly increased the reliability of our code as well as the productivity of the programmers involved in this project.

chemf: A purely functional chemistry toolkit

PubMed Central

2012-01-01

Background Although programming in a type-safe and referentially transparent style offers several advantages over working with mutable data structures and side effects, this style of programming has not seen much use in chemistry-related software. Since functional programming languages were designed with referential transparency in mind, these languages offer a lot of support when writing immutable data structures and side-effects free code. We therefore started implementing our own toolkit based on the above programming paradigms in a modern, versatile programming language. Results We present our initial results with functional programming in chemistry by first describing an immutable data structure for molecular graphs together with a couple of simple algorithms to calculate basic molecular properties before writing a complete SMILES parser in accordance with the OpenSMILES specification. Along the way we show how to deal with input validation, error handling, bulk operations, and parallelization in a purely functional way. At the end we also analyze and improve our algorithms and data structures in terms of performance and compare it to existing toolkits both object-oriented and purely functional. All code was written in Scala, a modern multi-paradigm programming language with a strong support for functional programming and a highly sophisticated type system. Conclusions We have successfully made the first important steps towards a purely functional chemistry toolkit. The data structures and algorithms presented in this article perform well while at the same time they can be safely used in parallelized applications, such as computer aided drug design experiments, without further adjustments. This stands in contrast to existing object-oriented toolkits where thread safety of data structures and algorithms is a deliberate design decision that can be hard to implement. Finally, the level of type-safety achieved by Scala highly increased the reliability of our code as well as the productivity of the programmers involved in this project. PMID:23253942

Integrating atlas and graph cut methods for right ventricle blood-pool segmentation from cardiac cine MRI

NASA Astrophysics Data System (ADS)

Dangi, Shusil; Linte, Cristian A.

2017-03-01

Segmentation of right ventricle from cardiac MRI images can be used to build pre-operative anatomical heart models to precisely identify regions of interest during minimally invasive therapy. Furthermore, many functional parameters of right heart such as right ventricular volume, ejection fraction, myocardial mass and thickness can also be assessed from the segmented images. To obtain an accurate and computationally efficient segmentation of right ventricle from cardiac cine MRI, we propose a segmentation algorithm formulated as an energy minimization problem in a graph. Shape prior obtained by propagating label from an average atlas using affine registration is incorporated into the graph framework to overcome problems in ill-defined image regions. The optimal segmentation corresponding to the labeling with minimum energy configuration of the graph is obtained via graph-cuts and is iteratively refined to produce the final right ventricle blood pool segmentation. We quantitatively compare the segmentation results obtained from our algorithm to the provided gold-standard expert manual segmentation for 16 cine-MRI datasets available through the MICCAI 2012 Cardiac MR Right Ventricle Segmentation Challenge according to several similarity metrics, including Dice coefficient, Jaccard coefficient, Hausdorff distance, and Mean absolute distance error.

Post-processing interstitialcy diffusion from molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Bhardwaj, U.; Bukkuru, S.; Warrier, M.

2016-01-01

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms.

Post-processing interstitialcy diffusion from molecular dynamics simulations

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

Bhardwaj, U., E-mail: haptork@gmail.com; Bukkuru, S.; Warrier, M.

2016-01-15

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures ismore » studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:.« less

Parallel CE/SE Computations via Domain Decomposition

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Jorgenson, Philip C. E.; Wang, Xiao-Yen; Chang, Sin-Chung

2000-01-01

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space-Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.

Comparison of multihardware parallel implementations for a phase unwrapping algorithm

NASA Astrophysics Data System (ADS)

Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

2018-04-01

Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

Modeling and optimum time performance for concurrent processing

NASA Technical Reports Server (NTRS)

Mielke, Roland R.; Stoughton, John W.; Som, Sukhamoy

1988-01-01

The development of a new graph theoretic model for describing the relation between a decomposed algorithm and its execution in a data flow environment is presented. Called ATAMM, the model consists of a set of Petri net marked graphs useful for representing decision-free algorithms having large-grained, computationally complex primitive operations. Performance time measures which determine computing speed and throughput capacity are defined, and the ATAMM model is used to develop lower bounds for these times. A concurrent processing operating strategy for achieving optimum time performance is presented and illustrated by example.

Modeling heterogeneous processor scheduling for real time systems

NASA Technical Reports Server (NTRS)

Leathrum, J. F.; Mielke, R. R.; Stoughton, J. W.

1994-01-01

A new model is presented to describe dataflow algorithms implemented in a multiprocessing system. Called the resource/data flow graph (RDFG), the model explicitly represents cyclo-static processor schedules as circuits of processor arcs which reflect the order that processors execute graph nodes. The model also allows the guarantee of meeting hard real-time deadlines. When unfolded, the model identifies statically the processor schedule. The model therefore is useful for determining the throughput and latency of systems with heterogeneous processors. The applicability of the model is demonstrated using a space surveillance algorithm.

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

NASA Technical Reports Server (NTRS)

Venter, Gerhard; Sobieszczanski-Sobieski, Jaroslaw

2005-01-01

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

Adapting high-level language programs for parallel processing using data flow

NASA Technical Reports Server (NTRS)

Standley, Hilda M.

1988-01-01

EASY-FLOW, a very high-level data flow language, is introduced for the purpose of adapting programs written in a conventional high-level language to a parallel environment. The level of parallelism provided is of the large-grained variety in which parallel activities take place between subprograms or processes. A program written in EASY-FLOW is a set of subprogram calls as units, structured by iteration, branching, and distribution constructs. A data flow graph may be deduced from an EASY-FLOW program.

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

Queues on a Dynamically Evolving Graph

NASA Astrophysics Data System (ADS)

Mandjes, Michel; Starreveld, Nicos J.; Bekker, René

2018-04-01

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between `up' and `down'. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues' time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links' outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

HeNCE: A Heterogeneous Network Computing Environment

DOE PAGES

Beguelin, Adam; Dongarra, Jack J.; Geist, George Al; ...

1994-01-01

Network computing seeks to utilize the aggregate resources of many networked computers to solve a single problem. In so doing it is often possible to obtain supercomputer performance from an inexpensive local area network. The drawback is that network computing is complicated and error prone when done by hand, especially if the computers have different operating systems and data formats and are thus heterogeneous. The heterogeneous network computing environment (HeNCE) is an integrated graphical environment for creating and running parallel programs over a heterogeneous collection of computers. It is built on a lower level package called parallel virtual machine (PVM).more » The HeNCE philosophy of parallel programming is to have the programmer graphically specify the parallelism of a computation and to automate, as much as possible, the tasks of writing, compiling, executing, debugging, and tracing the network computation. Key to HeNCE is a graphical language based on directed graphs that describe the parallelism and data dependencies of an application. Nodes in the graphs represent conventional Fortran or C subroutines and the arcs represent data and control flow. This article describes the present state of HeNCE, its capabilities, limitations, and areas of future research.« less

Parallel heuristics for scalable community detection

DOE PAGES

Lu, Hao; Halappanavar, Mahantesh; Kalyanaraman, Ananth

2015-08-14

Community detection has become a fundamental operation in numerous graph-theoretic applications. Despite its potential for application, there is only limited support for community detection on large-scale parallel computers, largely owing to the irregular and inherently sequential nature of the underlying heuristics. In this paper, we present parallelization heuristics for fast community detection using the Louvain method as the serial template. The Louvain method is an iterative heuristic for modularity optimization. Originally developed in 2008, the method has become increasingly popular owing to its ability to detect high modularity community partitions in a fast and memory-efficient manner. However, the method ismore » also inherently sequential, thereby limiting its scalability. Here, we observe certain key properties of this method that present challenges for its parallelization, and consequently propose heuristics that are designed to break the sequential barrier. For evaluation purposes, we implemented our heuristics using OpenMP multithreading, and tested them over real world graphs derived from multiple application domains. Compared to the serial Louvain implementation, our parallel implementation is able to produce community outputs with a higher modularity for most of the inputs tested, in comparable number or fewer iterations, while providing real speedups of up to 16x using 32 threads.« less

Using graph approach for managing connectivity in integrative landscape modelling

NASA Astrophysics Data System (ADS)

Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

2013-04-01

In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). OpenFLUID-landr library has been developed in order i) to be used with no GIS expert skills needed (common gis formats can be read and simplified spatial management is provided), ii) to easily develop adapted rules of landscape discretization and graph creation to follow spatialized model requirements and iii) to allow model developers to manage dynamic and complex spatial topology. Graph management in OpenFLUID are shown with i) examples of hydrological modelizations on complex farmed landscapes and ii) the new implementation of Geo-MHYDAS tool based on the OpenFLUID-landr library, which allows to discretize a landscape and create graph structure for the MHYDAS model requirements.

Distributed-Memory Fast Maximal Independent Set

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

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

The Maximal Independent Set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of MIS problems suggests the use of distributed-memory hardware as a cost-effective approach to providing necessary compute and memory resources. Luby proposed four randomized algorithms to solve the MIS problem. All those algorithms are designed focusing on shared-memory machines and are analyzed using the PRAM model. These algorithms do not have direct efficient distributed-memory implementations. In this paper, we extend two of Luby’s seminal MIS algorithms, “Luby(A)” and “Luby(B),” to distributed-memory execution, and we evaluatemore » their performance. We compare our results with the “Filtered MIS” implementation in the Combinatorial BLAS library for two types of synthetic graph inputs.« less

Parallel Architectures and Parallel Algorithms for Integrated Vision Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Choudhary, Alok Nidhi

1989-01-01

Computer vision is regarded as one of the most complex and computationally intensive problems. An integrated vision system (IVS) is a system that uses vision algorithms from all levels of processing to perform for a high level application (e.g., object recognition). An IVS normally involves algorithms from low level, intermediate level, and high level vision. Designing parallel architectures for vision systems is of tremendous interest to researchers. Several issues are addressed in parallel architectures and parallel algorithms for integrated vision systems.

SWAP-Assembler 2: Optimization of De Novo Genome Assembler at Large Scale

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

Meng, Jintao; Seo, Sangmin; Balaji, Pavan

2016-08-16

In this paper, we analyze and optimize the most time-consuming steps of the SWAP-Assembler, a parallel genome assembler, so that it can scale to a large number of cores for huge genomes with the size of sequencing data ranging from terabyes to petabytes. According to the performance analysis results, the most time-consuming steps are input parallelization, k-mer graph construction, and graph simplification (edge merging). For the input parallelization, the input data is divided into virtual fragments with nearly equal size, and the start position and end position of each fragment are automatically separated at the beginning of the reads. Inmore » k-mer graph construction, in order to improve the communication efficiency, the message size is kept constant between any two processes by proportionally increasing the number of nucleotides to the number of processes in the input parallelization step for each round. The memory usage is also decreased because only a small part of the input data is processed in each round. With graph simplification, the communication protocol reduces the number of communication loops from four to two loops and decreases the idle communication time. The optimized assembler is denoted as SWAP-Assembler 2 (SWAP2). In our experiments using a 1000 Genomes project dataset of 4 terabytes (the largest dataset ever used for assembling) on the supercomputer Mira, the results show that SWAP2 scales to 131,072 cores with an efficiency of 40%. We also compared our work with both the HipMER assembler and the SWAP-Assembler. On the Yanhuang dataset of 300 gigabytes, SWAP2 shows a 3X speedup and 4X better scalability compared with the HipMer assembler and is 45 times faster than the SWAP-Assembler. The SWAP2 software is available at https://sourceforge.net/projects/swapassembler.« less

Strong parameterization and coordination encirclements of graph of Penrose tiling vertices

NASA Astrophysics Data System (ADS)

Shutov, A. V.; Maleev, A. V.

2017-07-01

The coordination encirclements in a graph of Penrose tiling vertices have been investigated based on the analysis of vertice parameters. A strong parameterization of these vertices is developed in the form of a tiling of a parameter set in the region corresponding to different first coordination encirclements of vertices. An algorithm for constructing tilings of a set of parameters determining different coordination encirclements in a graph of Penrose tiling vertices of order n is proposed.

Very Large Graphs for Information Extraction (VLG) Detection and Inference in the Presence of Uncertainty

DTIC Science & Technology

2015-09-21

this framework, MIT LL carried out a one-year proof- of-concept study to determine the capabilities and challenges in the detection of anomalies in...extremely large graphs [5]. Under this effort, two real datasets were considered, and algorithms for data modeling and anomaly detection were developed...is required in a well-defined experimental framework for the detection of anomalies in very large graphs. This study is intended to inform future

Solution to the SLAM problem in low dynamic environments using a pose graph and an RGB-D sensor.

PubMed

Lee, Donghwa; Myung, Hyun

2014-07-11

In this study, we propose a solution to the simultaneous localization and mapping (SLAM) problem in low dynamic environments by using a pose graph and an RGB-D (red-green-blue depth) sensor. The low dynamic environments refer to situations in which the positions of objects change over long intervals. Therefore, in the low dynamic environments, robots have difficulty recognizing the repositioning of objects unlike in highly dynamic environments in which relatively fast-moving objects can be detected using a variety of moving object detection algorithms. The changes in the environments then cause groups of false loop closing when the same moved objects are observed for a while, which means that conventional SLAM algorithms produce incorrect results. To address this problem, we propose a novel SLAM method that handles low dynamic environments. The proposed method uses a pose graph structure and an RGB-D sensor. First, to prune the falsely grouped constraints efficiently, nodes of the graph, that represent robot poses, are grouped according to the grouping rules with noise covariances. Next, false constraints of the pose graph are pruned according to an error metric based on the grouped nodes. The pose graph structure is reoptimized after eliminating the false information, and the corrected localization and mapping results are obtained. The performance of the method was validated in real experiments using a mobile robot system.