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∗(2.3147k) time and polynomial space. We also show that this problem can be reduced to a quadratic kernel with O(k3) edges.