A PTAS for the minimum weighted dominating set problem with smooth weights on unit disk graphs

Xu Zhu, Wei Wang (), Shan Shan, Zhong Wang and Weili Wu
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Xu Zhu: Xi’an Jiaotong University
Wei Wang: Xi’an Jiaotong University
Shan Shan: The University of Texas at Dallas
Zhong Wang: The University of Texas at Dallas
Weili Wu: The University of Texas at Dallas

Journal of Combinatorial Optimization, 2012, vol. 23, issue 4, No 3, 443-450

Abstract: Abstract In the minimum weighted dominating set problem (MWDS), we are given a unit disk graph with non-negative weight on each vertex. The MWDS seeks a subset of the vertices of the graph with minimum total weight such that each vertex of the graph is either in the subset or adjacent to some nodes in the subset. A weight function is called smooth, if the ratio of the weights of any two adjacent nodes is upper bounded by a constant. MWDS is known to be NP-hard. In this paper, we give the first polynomial time approximation scheme (PTAS) for MWDS with smooth weights on unit disk graphs, which achieves a (1+ε)-approximation for MWDS, for any ε>0.

Keywords: Dominating set; Maximal independent set; Polynomial time approximation scheme; Unit disk graphs (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-010-9357-z

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