A self-stabilizing algorithm for maximal matching
Information Processing Letters
Maximal matching stabilizes in quadratic time
Information Processing Letters
Uniform Dynamic Self-Stabilizing Leader Election
IEEE Transactions on Parallel and Distributed Systems
Some optimal inapproximability results
Journal of the ACM (JACM)
Maximal matching stabilizes in time O(m)
Information Processing Letters
Dynamic and self-stabilizing distributed matching
Proceedings of the twenty-first annual symposium on Principles of distributed computing
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
Timestamping Messages in Synchronous Computations
ICDCS '02 Proceedings of the 22 nd International Conference on Distributed Computing Systems (ICDCS'02)
Some simple distributed algorithms for sparse networks
Distributed Computing
A distributed approach to dynamic autonomous agent placement for tracking moving targets with application to monitoring urban environments
Distributed weighted vertex cover via maximal matchings
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
A Self-stabilizing Approximation Algorithm for Vertex Cover in Anonymous Networks
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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A vertex cover of a graph is a subset of vertices such that each edge has at least one endpoint in the subset. Determining the minimum vertex cover is a well-known NP-complete problem in a sequential setting. Several techniques, e.g., depth-first search, a local ratio theorem, and semidefinite relaxation, have given good approximation algorithms. However, some of them cannot be applied to a distributed setting, in particular self-stabilizing algorithms. Thus only a 2-approximation solution based on a self-stabilizing maximal matching has been obviously known until now. In this paper we propose a new self-stabilizing vertex cover algorithm that achieves (2–1/Δ)-approximation ratio, where Δ is the maximum degree of a given network. We first introduce a sequential (2–1/Δ)-approximation algorithm that uses a maximal matching with the high-degree-first order of vertices. Then we present a self-stabilizing algorithm based on the same idea, and show that the output of the algorithm is the same as that of the sequential one.