New Distributed Algorithm for Connected Dominating Set in Wireless Ad Hoc Networks

Connected dominating set (CDS) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. In this paper, we first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms can not guarantee to generate a CDS of small size. Their message complexities can be as high as $O\left(n^{2}\right) $, and their time complexities may also be as large as $O\left(n^{2}\right) $ and $O\left(n^{3}\right) $. We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, $O\left(n\right) $ time complexity and $O\left(n\log n\right) $ message complexity. By establishing the $\Omega\left(n\log n\right) $ lower bound on the message complexity of any distributed algorithm for nontrivial CDS, our algorithm is thus message-optimal.