Distributed Low-Cost Backbone Formation for Wireless Ad Hoc Networks

Backbone has been used extensively in various aspects (e.g., routing, route maintenance, broadcast, scheduling) for wireless ad hoc or sensor networks recently. Previous methods are mostly designed to minimize the size of the backbone. However, in many applications, it is desirable to construct a backbone with small cost when each wireless node has a cost of being in the backbone. In this paper, we first show that previous methods specifically designed to minimize the backbone size may produce a backbone with large cost. We then propose an efficient distributed method to construct a weighted backbone with low cost. We prove that the total cost of the constructed backbone is within a small constant factor of the optimum for homogeneous networks when either the nodes’ costs are smooth or the network density is bounded. The total number of messages of our method is O(n) when the geometry information of each wireless node is known; the total number of messages is O(m) otherwise for a network of n devices and m communication links. We also show that the constructed backbone is efficient for unicast routing: the total cost (or hop) of the least cost (or hop) path connecting any two nodes using backbone is no more than 3 times of the least cost (or hop) path in the original communication graph.