A fast and simple randomized parallel algorithm for maximal matching
Information Processing Letters
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Journal of Algorithms
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Journal of the ACM (JACM)
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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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Distributed Computing
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ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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DISC'09 Proceedings of the 23rd international conference on Distributed computing
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COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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In this article, we consider the problem of computing a minimum-weight vertex-cover in an n-node, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(log n + log Ŵ) communication rounds, where Ŵ is the average vertex-weight. The previous best algorithm for this problem requires O(log n(log n + logŴ)) rounds and it is not fully distributed. For a maximal matching M in G, it is a well-known fact that any vertex-cover in G needs to have at least |M| vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting.