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Abstract

We present a polylogarithmic local computation matching algorithm which guarantees a (1 - ε)-approximation to the maximum matching in graphs of bounded degree.

Keywords

Local Computation Algortithms Sublinear Algorithms Approximation Algorithms Maximum Matching 

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References

  1. 1.
    Alon, N., Babai, L., Itai, A.: A fast and simple randomized algorithm for the maximal independent set problem. Journal of Algorithms 7, 567–583 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alon, N., Rubinfeld, R., Vardi, S., Xie, N.: Space-efficient local computation algorithms. In: Proc. 22nd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1132–1139 (2012)Google Scholar
  3. 3.
    Berge, C.: Two theorems in graph theory. Proceedings of the National Academy of Sciences of the United States of America 43(9), 842–844 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Czygrinow, A., Hanckowiak, M.: Distributed algorithm for better approximation of the maximum matching. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 242–251. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Edmonds, J.: Paths, trees, and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Hall, P.: On representatives of subsets. J. London Math. Soc. 10(1), 26–30 (1935)Google Scholar
  7. 7.
    Harvey, N.: Algebraic structures and algorithms for matching and matroid problems. In: Proc. 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 531–542 (2006)Google Scholar
  8. 8.
    Hoepman, J.-H., Kutten, S., Lotker, Z.: Efficient distributed weighted matchings on trees. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 115–129. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Hopcroft, J.E., Karp, R.M.: An N 5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing 2(4), 225–231 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Inf. Process. Lett. 22(2), 77–80 (1986)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: Proc. 17th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 980–989 (2006)Google Scholar
  12. 12.
    Kuhn, H.W.: The hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97 (1955)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lotker, Z., Patt-Shamir, B., Pettie, S.: Improved distributed approximate matching. In: Proc. 20th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 129–136 (2008)Google Scholar
  14. 14.
    Mansour, Y., Rubinstein, A., Vardi, S., Xie, N.: Converting online algorithms to local computation algorithms. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 653–664. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Mansour, Y., Vardi, S.: Local algorithmic mechanism design. Under submission elsewhereGoogle Scholar
  16. 16.
    Micali, S., Vazirani, V.V.: An \(O(\sqrt{|V|} |E|)\) algorithm for finding maximum matching in general graphs. In: Proc. 21st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 17–27 (1980)Google Scholar
  17. 17.
    Mucha, M., Sankowski, P.: Maximum matchings via gaussian elimination. In: FOCS, pp. 248–255 (2004)Google Scholar
  18. 18.
    Munkres, J.: Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics 5(1), 32–38 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Nguyen, H.N., Onak, K.: Constant-time approximation algorithms via local improvements. In: Proc. 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 327–336 (2008)Google Scholar
  20. 20.
    Rubinfeld, R., Tamir, G., Vardi, S., Xie, N.: Fast local computation algorithms. In: Proc. 2nd Symposium on Innovations in Computer Science (ICS), pp. 223–238 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yishay Mansour
    • 1
  • Shai Vardi
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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