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A Better Approximation Algorithm for Computing Connected Dominating Sets in Unit Ball Graphs
August 2010 (vol. 9 no. 8)
pp. 1108-1118
Donghyun Kim, University of Texas at Dallas, Richardson
Zhao Zhang, Xinjiang University, Urumqi
Xianyue Li, Lanzhou University, Lanzhou
Wei Wang, Xi'an Jiaotong University, Xi'an
Weili Wu, University of Texas at Dallas, Richardson
Ding-Zhu Du, University of Texas at Dallas, Richardson
A Virtual Backbone (VB) of a wireless network is a subset of nodes such that only VB nodes are responsible for routing-related tasks. Since a smaller VB causes less overhead, size is the primary quality factor of VB. Frequently, Unit Disk Graphs (UDGs) are used to model 2D homogeneous wireless networks, and the problem of finding minimum VBs in the networks is abstracted as Minimum Connected Dominating Set (MCDS) problem in UDGs. In some applications, the altitude of nodes can be hugely different and UDG cannot abstract the networks accurately. Then, Unit Ball Graph (UBG) can replace UDG. In this paper, we study how to construct quality CDSs in UBGs in distributed environments. We first give an improved upper bound of the number of independent nodes in a UBG, and use this result to analyze the Performance Ratio (PR) of our new centralized algorithm C-CDS-UBG, which computes CDSs in UBGs. Next, we propose a distributed algorithm D-CDS-UBG originated from C-CDS-UBG and analyze its message and time complexities. Our theoretical analysis shows that the PR of D-CDS-UBG is 14.937, which is better than current best, 22. Our simulations also show that D-CDS-UBG outperforms the competitor, on average.

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Index Terms:
Wireless networks, connected dominating sets, virtual backbones, unit ball graphs.
Citation:
Donghyun Kim, Zhao Zhang, Xianyue Li, Wei Wang, Weili Wu, Ding-Zhu Du, "A Better Approximation Algorithm for Computing Connected Dominating Sets in Unit Ball Graphs," IEEE Transactions on Mobile Computing, vol. 9, no. 8, pp. 1108-1118, Aug. 2010, doi:10.1109/TMC.2010.55
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