New parameterized algorithms for the edge dominating set problem

Authors:
Mingyu Xiao;Ton Kloks;Sheung-Hung Poon
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;Department of Computer Science, National Tsing Hua University, Taiwan;Department of Computer Science, National Tsing Hua University, Taiwan
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

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.