Tighter Approximation Bounds for Minimum CDS in Wireless Ad Hoc Networks

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 γc of a unit-disk graph plays the key role. The best-known relation between them is α ≤ 3 2 3 γc + 1. In this paper, we prove that α ≤ 3.4306γc + 4.8185. This relation leads to tighter upper bounds on the approximation ratios of two approximation algorithms proposed in the literature.