A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks

Authors:
Zhao Zhang;Xiaofeng Gao;Weili Wu;Ding-Zhu Du
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, People's Republic of China 830046;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75080;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75080;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75080
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

When homogeneous sensors are deployed into a three-dimensional space instead of a plane, the mathematical model for the sensor network is a unit ball graph instead of a unit disk graph. It is known that for the minimum connected dominating set in unit disk graph, there is a polynomial time approximation scheme (PTAS). However, that construction cannot be extended to obtain a PTAS for unit ball graph. In this paper, we will introduce a new construction, which gives not only a PTAS for the minimum connected dominating set in unit ball graph, but also improves running time of PTAS for unit disk graph.