Distributed Connected Dominating Set Construction in Geometric k-Disk Graphs

In this paper, we study the problem of minimum connected dominating set in geometric k-disk graphs. This research is motivated by the problem of virtual backbone construction in wireless ad hoc and sensor networks, where the coverage area of nodes are disks with different radii. We derive the size relationship of any maximal independent set and the minimum connected dominating set in geometric k-disk graphs, and apply it to analyze the performances of two distributed connected dominating set algorithms we propose in this paper. These algorithms have a bounded performance ratio and low communication overhead, and therefore have the potential to be applied in real ad hoc and sensor networks.