New Parameterized Algorithms for the Edge Dominating Set Problem

An edge dominating set of a graph G = (V,E) is a subset M ⊆ E of edges in the graph such that each edge in E − M is incident with at least one edge in M. In an instance of the parameterized edge dominating set problem we are given a graph G = (V,E) and an integer k and we are asked to decide whether G has an edge dominating set of size at most k. In this paper we show that the parameterized edge dominating set problem can be solved in O *(2.3147 k ) time and polynomial space. We also show that this problem can be reduced to a quadratic kernel with O(k 3) edges.