An Improved Algorithm for Parameterized Edge Dominating Set Problem

Abstract

An edge dominating set of a graph G = (V, E) is a subset M ⊆ E of edges such that each edge in E \M is incident to at least one edge in M. In this paper, we consider the parameterized edge dominating set problem which asks us to test whether a given graph has an edge dominating set with size bounded from above by an integer k or not, and we design an O^*(2.2351^k)-time and polynomial-space algorithm. This is an improvement over the previous best time bound of O^*(2.3147^k). We also show two corollaries: the parameterized weighted edge dominating set problem can be solved in O^*(2.2351^k) time and polynomial space; and a minimum edge dominating set of a graph G can be found in O^*(1.7957^τ) time where τ is the size of a minimum vertex cover of G