Efficient distributed weighted matchings on trees

Authors:
Jaap-Henk Hoepman;Shay Kutten;Zvi Lotker
Affiliations:
Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Faculty of Industrial Engineering and Management, Technion, Haifa, Israel;CWI, Amsterdam, The Netherlands
Venue:
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Year:
2006

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Abstract

In this paper, we study distributed algorithms to compute a weighted matching that have constant (or at least sub-logarithmic) running time and that achieve approximation ratio 2 + ε or better. In fact we present two such synchronous algorithms, that work on arbitrary weighted trees The first algorithm is a randomised distributed algorithm that computes a weighted matching of an arbitrary weighted tree, that approximates the maximum weighted matching by a factor 2 + ε. The running time is O(1). The second algorithm is deterministic, and approximates the maximum weighted matching by a factor 2 + ε, but has running time O(log* |V|). Our algorithms can also be used to compute maximum unweighted matchings on regular and almost regular graphs within a constant approximation