A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph

Connected Dominating Set is widely used as virtual backbone in wireless Ad-hoc and sensor networks to improve the performance of transmission and routing protocols. Based on special characteristics of Ad-hoc and sensor networks, we usually use unit disk graph to represent the corresponding geometrical structures, where each node has a unit transmission range and two nodes are said to be adjacent if the distance between them is less than 1. Since every Maximal Independent Set (MIS) is a dominating set and it is easy to construct, we can firstly find a MIS and then connect it into a Connected Dominating Set (CDS). Therefore, the ratio to compare the size of a MIS with a minimum CDS becomes a theoretical upper bound for approximation algorithms to compute CDS. In our paper, with the help of Voronoi diagram and Euler’s formula, we improved this upper bound, so that improved the approximations based on this relation.