An o*(1.4786n)-time algorithm for the maximum induced matching problem

Abstract

Given a graph G = (V,E) the MAXIMUM r-REGULAR INDUCED SUBGRAPH problem is to find a vertex set R ⊆ V of maximum cardinality such that G[R] is r-regular. An induced matching M ⊆ E in a graph G = (V,E) is a matching such that no two edges in M are joined by any third edge of the graph. The MAXIMUM INDUCED MATCHING problem is to find an induced matching of maximum cardinality. By definition the maximum induced matching problem is the maximum 1-regular induced subgraph problem. Gupta et al. gave an o(2n) time algorithm for solving the MAXIMUM r-REGULAR INDUCED SUBGRAPH problem. This algorithm solves the MAXIMUM INDUCED MATCHING problem in time O * (1.6957n) where n is the number of vertices in the input graph. In this paper, we show that the maximum induced matching problem can be reduced to the maximum independent set problem and we give a more efficient algorithm for the MAXIMUM INDUCED MATCHING problem running in time O * (1.4786n). © Springer-Verlag Berlin Heidelberg 2013.