Exact algorithms for edge domination

Abstract

In this paper we present a faster exact exponential time algorithm for the edge dominating set problem. Our algorithm uses O(1.3226n ) time and polynomial space. The algorithm combines an enumeration approach based on enumerating minimal vertex covers with the branch and reduce paradigm. Its time bound is obtained using the measure and conquer technique. The algorithm is obtained by starting with a slower algorithm which is refined stepwise. In this way a series of algorithms appears, each one slightly faster than the previous, resulting in the O(1.3226n ) time algorithm. The techniques also gives faster exact algorithms for: minimum weight edge dominating set, minimum (weight) maximal matching, matrix domination and the parametrised version of minimum weight maximal matching. © 2008 Springer-Verlag Berlin Heidelberg.