Two-Phased Approximation Algorithms 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 distributed algorithms for constructing a small CDS in wireless ad hoc networks have been proposed in the literature. The majority of these distributed 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 this paper, we prove that the approximation ratio of the two-phased algorithm in [10] is at most 7 1/3, improving upon the previous best-known approximation ratio of 7.6 due to [12]. We also propose a new two-phased approximation algorithm and prove that its approximation ratio is at most 6 7/18. Our analyses exploit an improved upper bound on the number independent points that can be packed in the neighborhood of a connected finite planar set.