An Algorithm to Determine the Sequence of Stable Connected Dominating Sets in Mobile Ad Hoc Networks

We show that given the complete knowledge of future topology changes, it is possible to determine the sequence of stable connected dominating sets (called the stable mobile connected dominating set) in a network session such that the number of CDS transitions is minimum. The algorithm to determine the mobile connected dominating set and the minimum number of CDS transitions is called OptCDSTrans and is based on a simple greedy approach: whenever a CDS is required, choose the CDS that will exist for the longest time. The above strategy is repeated over the duration of the network session. We prove that OptCDSTrans gives the optimal number of CDS transitions and simultaneously yields the stable mobile connected dominating set. We study the performance of OptCDSTrans in terms of number of CDS transitions and CDS size (the number of nodes constituting the CDS) for different conditions of node mobility and network density.