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

• Published in: Theoretical computer science Vol. 412; no. 40; pp. 5515 - 5526
• Main Authors: Manne, Fredrik, Mjelde, Morten, Pilard, Laurence, Tixeuil, Sébastien
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier 16.09.2011
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Computation; Computer Science; Computer science; control theory; systems; Exact sciences and technology; Graphs; Information retrieval. Graph; Matching; Miscellaneous; Theoretical computing; Maximum; Approximation; Computer theory; Sequential method; Maximum matching; Self-stabilizing algorithm; Approximation algorithm; Computing; Edge set; 2/3-approximation; Graph matching
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2011.05.019

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 the self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal ( 1 2 -approximation) matching in a general graph, as well as computing a 2 3 -approximation on more specific graph types. In this paper, we present the first self-stabilizing algorithm for finding a 2 3 -approximation to the maximum matching problem in a general graph. We show that our new algorithm, when run under a distributed adversarial daemon, stabilizes after at most O ( n 2 ) rounds. However, it might still use an exponential number of time steps.