(6 + ε)-Approximation for Minimum Weight Dominating Set in Unit Disk Graphs

Authors:
Xiaofeng Gao;Yaochun Huang;Zhao Zhang;Weili Wu
Affiliations:
Department of Computer Science, University of Texas at Dallas, USA;Department of Computer Science, University of Texas at Dallas, USA;College of Mathematics and System Sciences, Xingjiang University, China;Department of Computer Science, University of Texas at Dallas, USA
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

It was a long-standing open problem whether the minimum weightdominating set in unit disk graphs has a polynomial-timeconstant-approximation. In 2006, Ambühl et alsolvedthis problem by presenting a 72-approximation for the minimumweight dominating set and also a 89-approximation for the minimumweight connected dominating set in unit disk graphs. In this paper,we improve their results by giving a (6 +ε)-approximation for the minimum weight dominatingset and a (10 + ε)-approximation for the minimumweight connected dominating set in unit disk graphs whereεis any small positive number.