A tight analysis of the maximal matching heuristic

Authors:
Jean Cardinal;Martine Labbé;Stefan Langerman;Eythan Levy;Hadrien Mélot
Affiliations:
Université Libre de Bruxelles, Brussels, Belgium;Université Libre de Bruxelles, Brussels, Belgium;Université Libre de Bruxelles, Brussels, Belgium;Université Libre de Bruxelles, Brussels, Belgium;Université de Mons-Hainaut, Belgium
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

We study the worst-case performance of the maximal matching heuristic applied to the Minimum Vertex Cover and Minimum Maximal Matching problems, through a careful analysis of tight examples. We show that the tight worst-case approximation ratio is asymptotic to ${\rm min}\, \{2, 1/(1-\sqrt{1-\epsilon})\}$ for graphs with an average degree at least εn and to min {2, 1/ε} for graphs with a minimum degree at least εn.