Tighter Approximation Bounds for Minimum CDS in Wireless Ad Hoc Networks

Abstract

Connected dominating set (CDS) has a wide range of applications in wireless ad hoc networks. A number of approximation algorithms for constructing a small CDS in wireless ad hoc networks have been proposed in the literature. The majority of these algorithms follow a general two-phased approach. The first phase constructs a dominating set, and the second phase selects additional nodes to interconnect the nodes in the dominating set. In the performance analyses of these two-phased algorithms, the relation between the independence number α and the connected domination number γ _c of a unit-disk graph plays the key role. The best-known relation between them is $\alpha\leq3\frac{2}{3}\gamma_{c}+1$. In this paper, we prove that α ≤ 3.4306γ _c  + 4.8185. This relation leads to tighter upper bounds on the approximation ratios of two approximation algorithms proposed in the literature.

This work was partially supported by Research Grants Council of Hong Kong SAR under Project No. CityU 122807 and No. CityU 117408, and National Basic Research Program of China Grant 2007CB807900 and 2007CB807901. Peng-Jun Wan was supported in part by National Science Foundation of USA under grants CNS-0831831 and CNS-0916666.