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Computing maximum matching in parallel on bipartite graphs: worth the effort?

Published: 13 November 2011 Publication History

Abstract

We discuss parallel algorithms for computing maximum matchings in bipartite graphs on multithreaded computers, reporting for the first time, good speedups for the maximum cardinality matching problem. Experiments with serial matching algorithms have shown that their performance is sensitive to the order in which vertices are processed. In the execution of a multithreaded parallel algorithm for matching, variability in the order in which different threads process vertices is unavoidable. This sensitivity raises the possibility that different execution orderings might adversely affect the performance of parallel matching algorithms. In this paper, we answer this question by showing that good speedups are attainable by careful design of algorithms tuned to the characteristics of multithreaded architectures and the structure of the input graphs. We discuss preliminary results from parallel implementations of two key algorithms (Hopcroft-Karp and Pothen-Fan) and their variants on three multithreaded platforms (Cray XMT, AMD Opteron and Intel Nehalem) using a carefully chosen test set from real-world applications as well as synthetical graphs.

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I. S. Duff and J. Koster. On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM J. Matrix Anal. Appl., 22(4):973--996, 2000.
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J. Hopcroft and R. Karp. A n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput., 2:225--231, 1973.
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M. Karpinski and W. Rytter. Fast parallel algorithms for graph matching problems. Oxford University Press, Inc., New York, NY, USA, 1998.
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L. Lovasz. Matching Theory (North-Holland mathematics studies). Elsevier Science Ltd, 1986.
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F. Manne and R. H. Bisseling. A parallel approximation algorithm for the weighted maximum matching problem. In Proceedings of the 7th International Conference on Parallel Processing and Applied Mathematics, PPAM'07, pages 708--717. Springer-Verlag, 2008.
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Cited By

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  • (2022)Greedy Dissection Method for Shared Parallelism in Incomplete Factorization Within INMOST PlatformSupercomputing10.1007/978-3-030-92864-3_7(87-101)Online publication date: 3-Jan-2022
  • (2012)Multithreaded Algorithms for Matching in Graphs with Application to Data Analysis in Flow CytometryProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum10.1109/IPDPSW.2012.310(2494-2497)Online publication date: 21-May-2012

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    cover image ACM Conferences
    IA3 '11: Proceedings of the 1st Workshop on Irregular Applications: Architectures and Algorithms
    November 2011
    52 pages
    ISBN:9781450311212
    DOI:10.1145/2089142
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 13 November 2011

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    Author Tags

    1. graph algorithms
    2. matching
    3. multithreaded

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    • (2022)Greedy Dissection Method for Shared Parallelism in Incomplete Factorization Within INMOST PlatformSupercomputing10.1007/978-3-030-92864-3_7(87-101)Online publication date: 3-Jan-2022
    • (2012)Multithreaded Algorithms for Matching in Graphs with Application to Data Analysis in Flow CytometryProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum10.1109/IPDPSW.2012.310(2494-2497)Online publication date: 21-May-2012

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