Adapting connected d-hop dominating sets to topology changes in wireless ad hoc networks

In wireless ad hoc networks, a clustering structure can be a backbone for efficient communications. Simplicity in communications can be achieved when the clusters can more simply communicate with each other. One way to achieve this is to require that the clusterheads be connected. We would also like to be able to adapt quickly to small changes in the network. In graph-theoretic terminology, a minimum set of such clusterheads is a minimum connected d-hop dominating set. In this paper, we show that the problem of adapting minimum connected d-hop dominating sets to local topology changes in wireless ad hoc networks is NP-complete. We then propose a heuristic to adapt a given minimal connected d-hop dominating set to a topology change in the networks. A distributed implementation of the heuristic is also presented.