Approximation algorithms for maximum matchings in undirected graphs

Abstract : We propose heuristics for approximating the maximum cardinality matching on undirected graphs. Our heuristics are based on the theoretical body of a certain type of random graphs, and are made practical for real-life ones. The idea is based on judiciously selecting a subgraph of a given graph and obtaining a maximum cardinality matching on this subgraph. We show that the heuristics have an approximation guarantee of around 0.866 − log(n)/n for a graph with n vertices. Experiments for verifying the theoretical results in practice are provided.
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Submitted on : Thursday, March 29, 2018 - 11:16:51 PM
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Fanny Dufossé, Kamer Kaya, Ioannis Panagiotas, Bora Uçar. Approximation algorithms for maximum matchings in undirected graphs. CSC 2018 - SIAM Workshop on Combinatorial Scientific Computing, Jun 2018, Bergen, Norway. pp.56-65, ⟨10.1137/1.9781611975215.6⟩. ⟨hal-01740403v3⟩

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