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检索条件"主题词=Graph Algorithms"

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Scalable Single Source Shortest Path algorithms for Massively Parallel Systems

Scalable Single Source Shortest Path Algorithms for Massivel...

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IEEE 28th International Parallel & Distributed Processing Symposium (IPDPS)

作者： Chakaravarthy, Venkatesan T. Checconi, Fabio Petrini, Fabrizio Sabharwal, Yogish IBM Res India New Delhi India IBM Corp TJ Watson Res Ctr Armonk NY 10504 USA

ISBN: (纸本)9780769552071

In the single-source shortest path (SSSP) problem, we have to find the shortest paths from a source vertex v to all other vertices in a graph. In this paper, we introduce a novel parallel algorithm, derived from the Bellman-Ford and Delta-stepping algorithms. We employ various pruning techniques, such as edge classification and direction-optimization, to dramatically reduce inter-node communication traffic, and we propose load balancing strategies to handle higher-degree vertices. The extensive performance analysis shows that our algorithms work well on scale-free and real-world graphs. In the largest tested configuration, an R-MAT graph with 2(38) vertices and 2(42) edges on 32, 768 Blue Gene/Q nodes, we have achieved a processing rate of three Trillion Edges Per Second (TTEPS), a four orders of magnitude improvement over the best published results.

关键词： BFS Blue Gene/Q graph algorithms Parallelization SSSP Supercomputer graph algorithms supercomputer parallelization vertex head Shortest path algorithms parallel system BUNDESAMT FUER STRAHLENSCHUTZ Parallel algorithms scale-free shortest path

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Brief Announcement: Almost-Tight Approximation Distributed Algorithm for Minimum Cut 14

Brief Announcement: Almost-Tight Approximation Distributed A...

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ACM Symposium on Principles of Distributed Computing (PODC)

作者： Nanongkai, Danupon Univ Vienna Fac Comp Sci Vienna Austria

ISBN: (纸本)9781450329446

In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let lambda be the minimum cut. Our algorithm can compute lambda exactly in (O)over tilde ((root n + D) poly(lambda)) time, where n is the number of nodes (processors) in the network, D is the network diameter, and (O)over tilde hides poly log n. By a standard reduction, we can convert this algorithm into a (1+epsilon)-approximation (O)over tilde((root n + D)= poly(epsilon))-time algorithm. The latter result improves over the previous (2+epsilon)-approximation (O)over tilde((root n + D)= poly(epsilon))-time algorithm of Ghaffari and Kuhn (DISC 2013). Due to the lower bound of (Omega)over tilde(root n + D) by Das Sarma et al. (SICOMP 2013), this running time is tight up to a poly log n factor. Our algorithm is an extremely simple combination of Thorup's tree packing theorem [Combinatorica 2007], Kutten and Peleg's tree partitioning algorithm [J. algorithms 1998], and Karger's dynamic programming [JACM 2000].

关键词： distributed computing graph algorithms minimum cut time complexity CONGEST model

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Distributed Approximation algorithms for Weighted Shortest Paths 14

Distributed Approximation Algorithms for Weighted Shortest P...

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46th Annual ACM Symposium on Theory of Computing (STOC)

作者： Nanongkai, Danupon Brown Univ ICERM Providence RI 02912 USA Nanyang Technol Univ Singapore 637371 Singapore

ISBN: (纸本)9781450327107

A distributed network is modeled by a graph having n nodes (processors) and diameter D. We study the time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O(log n) bandwidth restriction on edges (the standard synchronous CONGEST model). The question whether approximation algorithms help speed up the shortest paths and distance computation (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (SSSP) and all-pairs shortest paths (APSP) in the weighted case. Our main result is an algorithm for SSS P. Previous results are the classic O(n)-time Bellman-Ford algorithm and an O(n(1/2+1/2k) +D)-time (8k inverted right perpendicularlog (k +1)inverted left perpendicular - 1)-approximation algorithm, for any integer k >= 1, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use O(.) to hide the O(poly log n) term.) We present an O(n(1/2)D(1/4) D) time (1 + o(1))-approximation algorithm for SSS P. This algorithm is sublinear-time as long as D is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When D is small, our running time matches the lower bound of Omega(n(1/2) D) by Das Sarma et al. (SICOMP 2012), which holds even when D = Theta(log n), up to a poly log n factor. As a by-product of our technique, we obtain a simple O(n)-time (1-1 o(1))-approximation algorithm for APSP, improving the previous a(n)-time O(1)-approximation algorithm following from the results of Lenzen and Patt-Shamir. We also prove a matching lower bound. Our techniques also yield an O(n(1/2)) time algorithm on fully-connected networks, whic

关键词： distributed computing graph algorithms single-source shortest paths all-pairs shortest paths time complexity CONGEST model lower bounds

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Counting Homomorphisms to Cactus graphs Modulo 2 31

Counting Homomorphisms to Cactus Graphs Modulo 2

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31st International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Gobel, Andreas Goldberg, Leslie Ann Richerby, David Univ Oxford Dept Comp Sci Oxford England

ISBN: (纸本)9783939897651

A homomorphism from a graph G to a graph H is a function from V(G) to V(H) that preserves edges. Many combinatorial structures that arise in mathematics and computer science can be represented naturally as graph homomorphisms and as weighted sums of graph homomorphisms. In this paper, we study the complexity of counting homomorphisms modulo 2. The complexity of modular counting was introduced by Papadimitriou and Zachos and it has been pioneered by Valiant who famously introduced a problem for which counting modulo 7 is easy but counting modulo 2 is intractable. Modular counting provides a rich setting in which to study the structure of homomorphism problems. In this case, the structure of the graph H has a big influence on the complexity of the problem. Thus, our approach is graph-theoretic. We give a complete solution for the class of cactus graphs, which are connected graphs in which every edge belongs to at most one cycle. Cactus graphs arise in many applications such as the modelling of wireless sensor networks and the comparison of genomes. We show that, for some cactus graphs H, counting homomorphisms to H modulo 2 can be done in polynomial time. For every other fixed cactus graph H, the problem is complete for the complexity class circle plus P which is a wide complexity class to which every problem in the polynomial hierarchy can be reduced (using randomised reductions). Determining which H lead to tractable problems can be done in polynomial time. Our result builds upon the work of Faben and Jerrum, who gave a dichotomy for the case in which H is a tree.

关键词： modular counting homomorphisms cactus graph graph algorithms

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Exploratory Equivalence in graphs: Definition and algorithms

Exploratory Equivalence in Graphs: Definition and Algorithms

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Federated Conference on Computer Science and Information Systems (FedCSIS)

作者： Mihelic, Jurij Fuerst, Luka Cibej, Uros Univ Ljubljana Fac Comp & Informat Sci SI-1000 Ljubljana Slovenia

ISBN: (纸本)9788360810583

Motivated by improving the efficiency of pattern matching on graphs, we define a new kind of equivalence on graph vertices. Since it can be used in various graph algorithms that explore graphs, we call it exploratory equivalence. The equivalence is based on graph automorphisms. Because many similar equivalences exist (some also based on automorphisms), we argue that this one is novel. For each graph, there are many possible exploratory equivalences, but for improving the efficiency of the exploration, some are better than others. To this end, we define a goal function that models the reduction of the search space in such algorithms. We describe two greedy algorithms for the underlying optimization problem. One is based directly on the definition using a straightforward greedy criterion, whereas the second one uses several practical speedups and a different greedy criterion. Finally, we demonstrate the huge impact of exploratory equivalence on a real application, i.e., graph grammar parsing.

关键词： Computer science Grammar Greedy algorithms Image color analysis Optimization Orbits Partitioning algorithms greedy algorithm Partitioning algorithms image colour analysis syntax computer science Eye Sockets Orbits equivalence graph algorithms Automorphism Line graph

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Load-Balanced Breadth-First Search on GPUs

Load-Balanced Breadth-First Search on GPUs

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15th International Conference on Web-Age Information Management (WAIM)

作者： Zhu, Zhe Li, Jianjun Li, Guohui Huazhong Univ Sci & Technol Sch Comp Sci & Technol Wuhan Peoples R China

ISBN: (纸本)9783319080109;9783319080093

Breadth-first search (BFS) is widely used in web link and social network analysis as well as other fields. The graphics Processing Unit (GPU) has been demonstrated to have great potential in accelerating graph algorithms through parallel processing. However, BFS is difficult to parallelize efficiently due to the irregular workload distribution, leading to load imbalance between threads. Previous work has proposed several strategies to alleviate the load imbalance but none of them solves this issue in general. This paper presents a new GPU BFS algorithm that focuses on full load balance. Each BFS iteration is decoupled into two phases: work redistribution and neighbor gathering. Work redistribution phase reorganizes the irregular workloads in order for the neighbor gathering phase to visit the vertices in a load-balanced way. The evaluation results show that the proposed approach achieves speedups of up to 39x and 1.42x over CPU sequential implementation and state-of-the-art GPU implementation respectively.

关键词： Breadth-first search GPU load balance graph algorithms parallel algorithms

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Join-Reachability Problems in Directed graphs

Join-Reachability Problems in Directed Graphs

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6th International Computer Science Symposium in Russia (CSR)

作者： Georgiadis, Loukas Nikolopoulos, Stavros D. Palios, Leonidas Univ Ioannina Dept Comp Sci GR-45110 Ioannina Greece

ISBN: (纸本)9783642207112

For a given collection of directed graphs we define the join-reachability graph of , denoted by , as the directed graph that, for any pair of vertices u and v, contains a path from u to v if and only if such a path exists in all graphs of . Our goal is to compute an efficient representation of . In particular, we consider two versions of this problem. In the explicit version we wish to construct the smallest join-reachability graph for . In the implicit version we wish to build an efficient data structure, in terms of space and query time, such that we can report fast the set of vertices that reach a query vertex in all graphs of . This problem is related to the well-studied reachability problem and is motivated by emerging applications of graph-structured databases and graph algorithms. We consider the construction of join-reachability structures for two graphs and develop techniques that can be applied to both the explicit and the implicit problems. First we present optimal and near-optimal structures for paths and trees. Then, based on these results, we provide efficient structures for planar graphs and general directed graphs.

关键词： algorithms Data structures graph algorithms Reachability Combinatorial complexity

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NVM-based Hybrid BFS with Memory Efficient Data Structure 2

NVM-based Hybrid BFS with Memory Efficient Data Structure

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IEEE International Conference on Big Data

作者： Iwabuchi, Keita Sato, Hitoshi Yasui, Yuichiro Fujisawa, Katsuki Matsuoka, Satoshi Tokyo Inst Technol Tokyo Japan Kyushu Univ Fukuoka Japan Japan Sci & Technol Agcy CREST Kawaguchi Saitama Japan

ISBN: (纸本)9781479956661

We introduce a memory efficient implementation for the NVM-based Hybrid BFS algorithm that merges redundant data structures to a single graph data structure, while offloading infrequent accessed graph data on NVMs based on the detailed analysis of access patterns, and demonstrate extremely fast BFS execution for large-scale unstructured graphs whose size exceed the capacity of DRAM on the machine. Experimental results of Kronecker graphs compliant to the graph500 benchmark on a 2-way INTEL Xeon E5-2690 machine with 256 GB of DRAM show that our proposed implementation can achieve 4.14 GTEPS for a SCALE31 graph problem with 2 3 1 vertices and 2 3 5 edges, whose size is 4 times larger than the size of graphs that the machine can accommodate only using DRAM with only 14.99 % performance degradation. We also show that the power efficiency of our proposed implementation achieves 11.8 MTEPS/W. Based on the implementation, we have achieved the 3rd and 4th position of the Green graph500 list (2014 June) in the Big Data category.

关键词： Breadth-first search graph algorithms NVM Memory architecture Extreme Big Data

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Sending Secrets Swiftly: Approximation algorithms for Generalized Multicast Problems

Sending Secrets Swiftly: Approximation Algorithms for Genera...

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41st International Colloquium on Automata, Languages and Programming

作者： Nikzad, Afshin Ravi, R. Stanford Univ MS&E Dept Stanford CA 94305 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

ISBN: (纸本)9783662439517

We consider natural generalizations of the minimum broadcast time problem under the telephone model, where a rumor from a root node must be sent via phone calls to the whole graph in the minimum number of rounds;the telephone model implies that the set of edges involved in communicating in a round form a matching. The extensions we consider involve generalizing the number of calls that a vertex may participate in (the capacitated version), allowing conference calls (the hyperedge version) as well as a new multicommodity version we introduce where the rumors are no longer from a single node but from different sources and intended for specific destinations (the multicommodity version). Based on the ideas from[6,7], we present a very simple greedy algorithm for the basic multicast problem with logarithmic performance guarantee and adapt it to the extensions to design typically polylogarithmic approximation algorithms. For the multi-commodity version, we give the first approximation algorithm with performance ratio 2(O(log log k) (root log k)) for k source-sink pairs. We provide nearly matching lower bounds for the hypercasting problem. For the multicommodity multicasting problem, we present improved guarantees for other variants involving asymmetric capacities, small number of terminals and with larger additive guarantees.

关键词： approximation algorithms graph algorithms b-matching LP rounding

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Polynomial-Time algorithms for Energy Games with Special Weight Structures

Polynomial-Time Algorithms for Energy Games with Special Wei...

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20th Annual European Symposium on algorithms (ESA)

作者： Chatterjee, Krishnendu Henzinger, Monika Krinninger, Sebastian Nanongkai, Danupon IST Austria Klosterneuburg Austria Univ Vienna Fac Comp Sci Vienna Austria Nanyang Technol Univ Singapore 639798 Singapore

ISBN: (纸本)9783642330896

Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NPa (c) co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.

关键词： graph algorithms Polynomial-time algorithms Turn-based infinite duration games Energy games Mean-payoff games

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