Introduction

Most of the methods developed in the literature for backbone construction try to minimize the number of cluster-heads; i.e., the number of nodes in the backbone. However, in many applications of wireless ad hoc networks, minimizing the size of the backbone is not sufficient. For example, different wireless nodes may have different costs for serving as a cluster-head because of device differences, power capacities, and information loads to be processed. Therefore, in the rest of this chapter, for succinctness of presentation, we assume that each wireless node has a generic cost (or weight). The cost may also represent the fitness or priority of each node to be a cluster-head. Lower cost means higher priority. In practice, cost could represent the power-consumption rate of this node if a backbone with small power consumption is needed; the robustness of this node if a fault-tolerant backbone is needed; or a function of its security level if a secure backbone is needed. Y. Wang et al. (2005a) studied how to construct a sparse backbone efficiently for a set of weighted wireless nodes such that the total cost of the backbone is approximately minimized and there is a cost (or hops) efficient route connecting every pair of wireless nodes via the constructed network backbone.