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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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Dates and versions

hal-01740403 , version 1 (21-03-2018)
hal-01740403 , version 2 (22-03-2018)
hal-01740403 , version 3 (29-03-2018)

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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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