New results on polynomial inapproximability and fixed parameter approximability of edge dominating set

Bruno Escoffier (1) , Jérôme Monnot (2) , Vangelis Th. Paschos (2) , Mingyu Xiao (3)

1 RO - Recherche Opérationnelle
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 School of Computer Science and Technology, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

An edge dominating set in a graph G = (V, E) is a subset S of edges such that each edge in E − S is adjacent to at least one edge in S. The edge dominating set problem, to find an edge dominating set of minimum size, is a basic and important NP-hard problem that has been extensively studied in approximation algorithms and parameterized complexity. In this paper, we present improved hardness results and parameterized approximation algorithms for edge dominating set. More precisely, we first show that it is NP-hard to approximate edge dominating set in polynomial time within a factor better than 1.18. Next, we give a parameterized approximation schema (with respect to the standard parameter) for the problem and, finally, we develop an O * (1.821 τ)-time exact algorithm where τ is the size of a minimum vertex cover of G.

Domaines: Informatique [cs]; Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Bruno Escoffier, Jérôme Monnot, Vangelis Th. Paschos, Mingyu Xiao. New results on polynomial inapproximability and fixed parameter approximability of edge dominating set. Theory of Computing Systems, 2015, 56 (2), pp.330-346. ⟨10.1007/s00224-014-9549-5⟩. ⟨hal-01926689⟩