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ItemParallel Shortest Path Algorithms for Solving Large-Scale Instances(Georgia Institute of Technology, 2006-08-30) Madduri, Kamesh ; Bader, David A. ; Berry, Jonathan W. ; Crobak, Joseph R.We present an experimental study of parallel algorithms for solving the single source shortest path problem with non-negative edge weights (NSSP) on large-scale graphs. We implement Meyer and Sander's Δ-stepping algorithm and report performance results on the Cray MTA-2, a multithreaded parallel architecture. The MTA-2 is a high-end shared memory system offering two unique features that aid the efficient implementation of irregular parallel graph algorithms: the ability to exploit fine-grained parallelism, and low-overhead synchronization primitives. Our implementation exhibits remarkable parallel speedup when compared with a competitive sequential algorithm, for low-diameter sparse graphs. For instance, Δ-stepping on a directed scale-free graph of 100 million vertices and 1 billion edges takes less than ten seconds on 40 processors of the MTA-2, with a relative speedup of close to 30. To our knowledge, these are the first performance results of a parallel NSSP problem on realistic graph instances in the order of billions of vertices and edges.
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ItemParallel Algorithms for Evaluating Centrality Indices in Real-World Networks(Georgia Institute of Technology, 2006-04-14) Bader, David A. ; Madduri, KameshThis paper discusses fast parallel algorithms for evaluating several centrality indices frequently used in complex network analysis. These algorithms have been optimized to exploit properties typically observed in real-world large scale networks, such as the low average distance, high local density, and heavy-tailed power law degree distributions. We test our implementations on real datasets such as the web graph, protein-interaction networks, movie-actor and citation networks, and report impressive parallel performance for evaluation of the computationally intensive centrality metrics (betweenness and closeness centrality) on high-end shared memory symmetric multiprocessor and multithreaded architectures. To our knowledge, these are the first parallel implementations of these widely-used social network analysis metrics. We demonstrate that it is possible to rigorously analyze networks three orders of magnitude larger than instances that can be handled by existing network analysis (SNA) software packages. For instance, we compute the exact betweenness centrality value for each vertex in a large US patent citation network (3 million patents, 16 million citations) in 42 minutes on 16 processors, utilizing 20GB RAM of the IBM p5 570. Current SNA packages on the other hand cannot handle graphs with more than hundred thousand edges.
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ItemDesigning Multithreaded Algorithms for Breadth-First Search and st-connectivity on the Cray MTA-2(Georgia Institute of Technology, 2006-02-26) Bader, David A. ; Madduri, KameshGraph abstractions are extensively used to understand and solve challenging computational problems in various scientific and engineering domains. They have particularly gained prominence in recent years for applications involving large-scale networks. In this paper, we present fast parallel implementations of three fundamental graph theory problems, Breadth-First Search, st-connectivity and shortest paths for unweighted graphs, on multithreaded architectures such as the Cray MTA-2. The architectural features of the MTA-2 aid the design of simple, scalable and high-performance graph algorithms. We test our implementations on large scale-free and sparse random graph instances, and report impressive results, both for algorithm execution time and parallel performance. For instance, Breadth-First Search on a scale-free graph of 200 million vertices and 1 billion edges takes less than 5 seconds on a 40-processor MTA-2 system with an absolute speedup of close to 30. This is a significant result in parallel computing, as prior implementations of parallel graph algorithms report very limited or no speedup on irregular and sparse graphs, when compared to the best sequential implementation.
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ItemDesign and Implementation of the HPCS Graph Analysis Benchmark on Symmetric Multiprocessors(Georgia Institute of Technology, 2006-02-25) Bader, David A. ; Madduri, KameshGraph theoretic problems are representative of fundamental computations in traditional and emerging scientific disciplines like scientific computing and computational biology, as well as applications in national security. We present our design and implementation of a graph theory application that supports the kernels from the Scalable Synthetic Compact Applications (SSCA) benchmark suite, developed under the DARPA High Productivity Computing Systems (HPCS) program. This synthetic benchmark consists of four kernels that require irregular access to a large, directed, weighted multi-graph. We have developed a parallel implementation of this bench- mark in C using the POSIX thread library for commodity symmetric multiprocessors (SMPs). In this paper, we primarily discuss the data layout choices and algorithmic design issues for each kernel, and also present execution time and benchmark validation results.