Journal of Combinatorial Optimization

, Volume 11, Issue 3, pp 279–290

Approximation hardness of edge dominating set problems

Article

DOI: 10.1007/s10878-006-7908-0

Cite this article as:
Chlebík, M. & Chlebíková, J. J Comb Optim (2006) 11: 279. doi:10.1007/s10878-006-7908-0

Abstract

We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, MINIMUM EDGE DOMINATING SET and MINIMUM MAXIMAL MATCHING. We show that it is NP-hard to approximate the solution of both problems to within any constant factor smaller than \({\frac{7}{6}}\). The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs.

Keywords

Minimum edge dominating setMinimum maximal matchingApproximation lower boundBounded degree graphsEverywhere dense graphs

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Department of Informatics Education, Faculty of Mathematics, Physics, and InformaticsComenius UniversityBratislavaSlovakia