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Fast Distributed Approximation Algorithm for the Maximum Matching Problem in Bounded Arboricity Graphs

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

We give a deterministic distributed approximation algorithm for the maximum matching problem in graphs of bounded arboricity. Specifically, given 0 < ε< 1 and a positive integer a, the algorithm finds a matching of size at least (1 − ε)m(G), where m(G) is the size of the maximum matching in an n-vertex graph G with arboricity at most a. The algorithm runs in O(log* n) rounds in the message passing model and it is the first sublogarithmic algorithm for the problem on such a wide class of graphs. Moreover, the result implies that the known \(\Omega(\sqrt{\log n/\log\log n})\) lower bound on the time complexity for a constant or polylogarithmic approximation does not hold for graphs of bounded arboricity.

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Author information

Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA

    Andrzej Czygrinow

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    Michał Hańćkowiak & Edyta Szymańska

Authors
  1. Andrzej Czygrinow
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  2. Michał Hańćkowiak
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  3. Edyta Szymańska
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Czygrinow, A., Hańćkowiak, M., Szymańska, E. (2009). Fast Distributed Approximation Algorithm for the Maximum Matching Problem in Bounded Arboricity Graphs. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_68

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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