An Improved Algorithm for Parameterized Edge Dominating Set Problem

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)-time and polynomial-space algorithm. This is an improvement over the previous best time bound of O(2.3147). We also show two corollaries: the parameterized weighted edge dominating set problem can be solved in O(2.2351) time and polynomial space; and a minimum edge dominating set of a graph G can be found in O(1.7957 ) time where τ is the size of a minimum vertex cover of G. Submitted: March 2015 Reviewed: July 2015 Revised: November 2015 Accepted: November 2015 Final: January 2016 Published: Fabruray 2016 Article type: Regular paper Communicated by: M. S. Rahman and E. Tomita A preliminary version of this paper was presented at the 9th International Workshop on Algorithms and Computation (WALCOM 2015) [7] E-mail addresses: [email protected] (Ken Iwaide) [email protected] (Hiroshi Nag-