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A Self-stabilizing \(\frac{2}{3}\)-Approximation Algorithm for the Maximum Matching Problem

  • Fredrik Manne
  • Morten Mjelde
  • Laurence Pilard
  • Sébastien Tixeuil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5340)

Abstract

The matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal (\(\frac{1}{2}\)-approximation) matching in a general graph, as well as computing a \(\frac{2}{3}\)-approximation on more specific graph types. In the following we present the first self-stabilizing algorithm for finding a \(\frac{2}{3}\)-approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and O(n 2) rounds under a distributed fair daemon, where n is the number of nodes in the graph.

Keywords

Self-stabilizing algorithm \(\frac{2}{3}\)-Approximation Maximum matching 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Fredrik Manne
    • 1
  • Morten Mjelde
    • 1
  • Laurence Pilard
    • 2
  • Sébastien Tixeuil
    • 3
  1. 1.University of BergenNorway
  2. 2.University of Franche ComtéFrance
  3. 3.LIP6 & INRIA Grand LargeUniversité Pierre et Marie CurieParis 6France

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