Facing the Multicore - Challenge II pp 108-119

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7174) | Cite as

A GPU Algorithm for Greedy Graph Matching

  • Bas O. Fagginger Auer
  • Rob H. Bisseling

Abstract

Greedy graph matching provides us with a fast way to coarsen a graph during graph partitioning. Direct algorithms on the CPU which perform such greedy matchings are simple and fast, but offer few handholds for parallelisation. To remedy this, we introduce a fine-grained shared-memory parallel algorithm for maximal greedy matching, together with an implementation on the GPU, which is faster (speedups up to 6.8 for random matching and 5.6 for weighted matching) than the serial CPU algorithms and produces matchings of similar (random matching) or better (weighted matching) quality.

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References

  1. 1.
    Aykanat, C., Pinar, A., Çatalyürek, U.V.: Permuting sparse rectangular matrices into block-diagonal form. SIAM J. Sci. Comput. 25(6), 1860–1879 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bader, D.A., Sanders, P., Wagner, D., Meyerhenke, H., Hendrickson, B., Johnson, D.S., Walshaw, C., Mattson, T.G.: 10th DIMACS implementation challenge - graph partitioning and graph clustering (2012), http://www.cc.gatech.edu/dimacs10/index.shtml
  3. 3.
    Bell, N., Garland, M.: Cusp: Generic parallel algorithms for sparse matrix and graph computations, version 0.1.0 (2010), http://cusp-library.googlecode.com
  4. 4.
    Bertsekas, D.P.: A distributed asynchronous relaxation algorithm for the assignment problem. In: 24th IEEE CDC, vol. 24, pp. 1703–1704 (1985)Google Scholar
  5. 5.
    Çatalyürek, U.V., Aykanat, C.: Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans. Par. Dist. Syst. 10(7), 673–693 (1999)CrossRefGoogle Scholar
  6. 6.
    Davis, T.A., Hu, Y.: The University of Florida Sparse Matrix Collection. ACM TOMS 38(1), 1:1–1:25 (2011)Google Scholar
  7. 7.
    Grigori, L., Boman, E.G., Donfack, S., Davis, T.A.: Hypergraph-based unsymmetric nested dissection ordering for sparse LU factorization. SIAM J. Sci. Comput. 32(6), 3426–3446 (2010)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Her, J.H., Pellegrini, F.: Efficient and scalable parallel graph partitioning. Parallel Computing (2010)Google Scholar
  9. 9.
    Kahng, A.B., Reda, S.: Match twice and stitch: a new TSP tour construction heuristic. Operations Research Letters 32(6), 499–509 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Karp, R.M., Sipser, M.: Maximum matchings in sparse random graphs. In: Proc. 22nd FOCS, pp. 364–375 (1981)Google Scholar
  11. 11.
    Langguth, J., Manne, F., Sanders, P.: Heuristic initialization for bipartite matching problems. J. Exp. Algorithmics 15(1.3), 1.1–1.22 (2010)Google Scholar
  12. 12.
    Manne, F., Bisseling, R.H.: A Parallel Approximation Algorithm for the Weighted Maximum Matching Problem. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 708–717. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Patwary, M.A., Bisseling, R.H., Manne, F.: Parallel greedy graph matching using an edge partitioning approach. In: Proc. HLPP 2010, pp. 45–54. ACM (2010)Google Scholar
  14. 14.
    Preis, R.: Analyses and design of efficient graph partitioning methods. HNI-Verlagsschriftenreihe, Heinz Nixdorf Inst. Univ. Paderborn (2001)Google Scholar
  15. 15.
    Rivest, R.L.: The MD5 message-digest algorithm, Internet RFC 1321 (1992)Google Scholar
  16. 16.
    Segev, D.L., Gentry, S.E., Warren, D.S., Reeb, B., Montgomery, R.A.: Kidney paired donation and optimizing the use of live donor organs. JAMA 293(15), 1883–1890 (2005)CrossRefGoogle Scholar
  17. 17.
    Vasconcelos, C.N., Rosenhahn, B.: Bipartite Graph Matching Computation on GPU. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds.) EMMCVPR 2009. LNCS, vol. 5681, pp. 42–55. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Vastenhouw, B., Bisseling, R.H.: A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Rev. 47(1), 67–95 (2005)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Xing, G., Lu, C., Zhang, Y., Huang, Q., Pless, R.: Minimum power configuration for wireless communication in sensor networks. ACM Trans. Sen. Netw. 3(2) (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bas O. Fagginger Auer
    • 1
  • Rob H. Bisseling
    • 1
  1. 1.Mathematics InstituteUtrecht UniversityUtrechtThe Netherlands

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