A Tight Analysis of the Maximal Matching Heuristic

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 min{2, 1/(1 − √ 1 − )} for graphs with an average degree at least n and to min{2, 1/ } for graphs with a minimum degree at least n. These bounds apply to both problems and are obtained through a careful analysis of the tight examples.

• Type: Conference
• Year: 2005
• Where: COCOON
• Authors: Jean Cardinal, Martine Labbé, Stefan Langerman, Eythan Levy, Hadrien Mélot
• Keywords: COCOON 2005, Maximal Matching, Minimum Maximal Matching, Tight Worst-case Approximation