Abstract
We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms.
We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors.
The authors wish to thank HPC-Europe, the Dutch supercomputing centre SARA, NCF, the BSIK/BRICKS MSV1-2 program, and the NFR funded Parcomb project for financial support.
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References
Avis, D.: A survey of heuristics for the weighted matching problem. Networks 13, 475–493 (1983)
Bisseling, R.H.: Parallel Scientific Computation: A Structured Approach Using BSP and MPI. Oxford University Press, Oxford (2004)
Davis, T.: University of Florida sparse matrix collection. NA Digest 92(42) (October 16, 1994), NA Digest 96(28) (July 23, 1996), NA Digest 97(23) (June 7, 1997), http://www.cise.ufl.edu/research/sparse/matrices
Drake, D.E., Hougardy, S.: A linear-time approximation algorithm for weighted matchings in graphs. ACM Transactions on Algorithms 1, 107–122 (2005)
Duff, I.S., Koster, J.: The design and use of algorithms for permuting large entries to the diagonal of sparse matrices. SIAM J. Matrix Anal. Appl. 20, 889–901 (1999)
Duff, I.S., Koster, J.: On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM J. Matrix Anal. Appl. 22, 973–996 (2001)
Grama, A., Gupta, A., Karypis, G., Kumar, V.: Introduction to Parallel Computing, 2nd edn. Addison-Wesley, Reading (2003)
Hoepman, J.-H.: Simple distributed weighted matchings, arXiv:cs/0410047v1 (2004)
Karypis, G., Kumar, V.: Metis, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Version 4.0 (1998)
Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15, 1036–1053 (1986)
Pettie, S., Sanders, P.: A simpler linear time 2/3 − ε approximation for maximum weight matching. Inf. Process. Lett. 91, 271–276 (2004)
Preis, R.: Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 259–269. Springer, Heidelberg (1999)
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Manne, F., Bisseling, R.H. (2008). A Parallel Approximation Algorithm for the Weighted Maximum Matching Problem . In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_74
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DOI: https://doi.org/10.1007/978-3-540-68111-3_74
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