A Constant Factor Localized Algorithm for Computing Connected Dominating Sets in Wireless Sensor Networks

Connected dominating sets ($\CDS$s) are probably the most common way of constructing virtual backbones for broadcasting operation in wireless sensor networks. This is because such backbones guarantee to reduce unnecessary message transmissions or flooding in the network. In this paper we propose a simple localized algorithm to construct a \text it{small}-sized $\CDS$. Considering the sensors deployed in the plane, our main idea is based on the computation of convex hulls of sensor nodes (nodes are considered points in the plane) in a localized manner and a simple coloring scheme, which produces a $\CDS$ in unit disk graphs whose size is at most $38*|\MCDS|$ where $|\MCDS|$ is the size of a minimum $\CDS$. To the best of our knowledge, this is a significant improvement over the best published results in the same context \cite{Che}. We also analyze grids and trees to compute the exact approximation ratios for the problem. We show that our algorithm produces an optimal $\CDS$ if the graph is a tree and in the case of grids the approximation factor is $2$.