New parameterized algorithms for edge dominating set

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