Tighter Approximation Bounds for Minimum CDS in Unit Disk Graphs

Connected dominating set (CDS) in unit disk graphs has a wide range of applications in wireless ad hoc networks. A number of approximation algorithms for constructing a small CDS in unit disk graphs 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 a ￡ 3frac23g_c+1alphaleq3frac{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.