A $(2 - c \frac{\log {n}}{n})$ Approximation Algorithm for the Minimum Maximal Matching Problem

  • Authors:

  • Zvi Gotthilf;Moshe Lewenstein;Elad Rainshmidt

  • Affiliations:

  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel 52900;Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel 52900;Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel 52900

  • Venue:
  • Approximation and Online Algorithms
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider the problem of finding a maximal matching of minimum size, given an unweighted general graph. This problem is a well studied and it is known to be NP-hard even for some restricted classes of graphs. Moreover, in case of general graphs, it is NP-hard to approximate the Minimum Maximal Matching (shortly MMM) within any constant factor smaller than $\frac{7}{6}$. The current best known approximation algorithm is the straightforward algorithm which yields an approximation ratio of 2. We propose the first nontrivial algorithm yields an approximation ratio of $2 - c \frac{\log{n}}{n}$, for an arbitrarily positive constant c . Our algorithm is based on the local search technique and utilizes an approximate solution of the Minimum Weighted Maximal Matching problem in order to achieve the desirable approximation ratio.