A self-stabilizing 2/3-approximation algorithm for the maximum matching problem

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 when run under the distributed adversarial daemon, stabilizes after at most $O(n^2)$ rounds. However, it might still use an exponential number of time steps.
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Submitted on : Thursday, May 21, 2015 - 10:50:01 AM
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Fredrik Manne, Morten Mjelde, Laurence Pilard, Sébastien Tixeuil. A self-stabilizing 2/3-approximation algorithm for the maximum matching problem. Theoretical Computer Science, Elsevier, 2011, 412 (40), pp.5515-5526. ⟨10.1016/j.tcs.2011.05.019⟩. ⟨hal-01154122⟩

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