PTAS for the minimum weighted dominating set in growth bounded graphs

Authors:
Zhong Wang;Wei Wang;Joon-Mo Kim;Bhavani Thuraisingham;Weili Wu
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083;Department of Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China 710049;Dankook University, Seoul, Korea;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

The minimum weighted dominating set (MWDS) problem is one of the classic NP-hard optimization problems in graph theory with applications in many fields such as wireless communication networks. MWDS in general graphs has been showed not to have polynomial-time constant-approximation if $${\mathcal{NP} \neq \mathcal{P}}$$ . Recently, several polynomial-time constant-approximation SCHEMES have been designed for MWDS in unit disk graphs. In this paper, using the local neighborhood-based scheme technique, we present a PTAS for MWDS in polynomial growth bounded graphs with bounded degree constraint.