A Self-Stabilizing 2 3 -Approximation Algorithm for the Maximum Matching Problem. Fredrik Manne * Morten Mjelde * Laurence Pilard † S´ebastien Tixeuil ‡ 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 ( 1 2 - approximation) matching in a general graph, as well as computing a 2 3 -approximation on more specific graph types. In the following 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 stabilizes in at most exponential time under a dis- tributed adversarial daemon. Keywords: Self-stabilizing algorithm, 2 3 -Approximation, Maximum match- ing. 1 Introduction A matching in a graph G =(V,E) is a subset M of E such that no pair of edges in M have common endpoints. We say that two nodes v and w are matched if the edge (v,w) is in M . A matching M is maximal if no proper superset of M is also a matching. A matching M is maximum if there does not exists any matching with cardinality larger than |M |. While there exists sequential algorithms for computing a maximum matching in polynomial time, the complexity of such algorithms renders them impractical in many * University of Bergen, Norway. E-mail: {fredrikm, mortenm}@ii.uib.no. † University of Franche Comt´e, France. E-mail: laurence.pilard@iut-bm.univ-fcomte.fr ‡ LIP6 & INRIA Grand Large, Universit´e Pierre et Marie Curie - Paris 6, France. E-mail: tixeuil@lri.fr 1