A fast and simple randomized parallel algorithm for maximal matching
Information Processing Letters
A primal-dual parallel approximation technique applied to weighted set and vertex covers
Journal of Algorithms
Greed is good: approximating independent sets in sparse and bounded-degree graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
On the Distributed Complexity of Computing Maximal Matchings
SIAM Journal on Discrete Mathematics
Some simple distributed algorithms for sparse networks
Distributed Computing
Distributed and parallel algorithms for weighted vertex cover and other covering problems
Proceedings of the 28th ACM symposium on Principles of distributed computing
Approximation of self-stabilizing vertex cover less than 2
SSS'05 Proceedings of the 7th international conference on Self-Stabilizing Systems
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In this paper 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 ${\mathrm{O}}(\log n + \log \hat{W})$ communication rounds, where $\hat{W}$ is the average vertex-weight. The previous best algorithm for this problem requires ${\mathrm{O}}(\log n(\log n + \log \hat{W}))$ 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.