Extended dominating set and its applications in ad hoc networks using cooperative communication

We propose a notion of an extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2-hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates diversity and combats the effects of fading. We first show the NP-completeness of the minimum extended dominating set problem. Then, several heuristic algorithms, global and local, for constructing a small extended dominating set are proposed. These are nontrivial extensions of the existing algorithms for the regular dominating set problem. The application of the extended dominating set in efficient broadcasting is also discussed. The performance analysis includes an analytical study in terms of approximation ratio and a simulation study of the average size of the extended dominating set derived from the proposed algorithms.