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A Local Computation Approximation Scheme to Maximum Matching

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2013, RANDOM 2013)

Abstract

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

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  5. Edmonds, J.: Paths, trees, and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hall, P.: On representatives of subsets. J. London Math. Soc. 10(1), 26–30 (1935)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Inf. Process. Lett. 22(2), 77–80 (1986)

    Article  MathSciNet  Google Scholar 

  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. Kuhn, H.W.: The hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97 (1955)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  15. Mansour, Y., Vardi, S.: Local algorithmic mechanism design. Under submission elsewhere

    Google Scholar 

  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. Mucha, M., Sankowski, P.: Maximum matchings via gaussian elimination. In: FOCS, pp. 248–255 (2004)

    Google Scholar 

  18. Munkres, J.: Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics 5(1), 32–38 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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 

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Mansour, Y., Vardi, S. (2013). A Local Computation Approximation Scheme to Maximum Matching. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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