Abstract

Backbone has been used extensively in various aspects (e.g., rout-ing, route maintenance, broadcast, scheduling) for wireless net-works. Previous methods are mostly designed to minimize the backbone size. 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 a large cost. We then propose an efficient distributed method to construct a weighted sparse back-bone with low cost. We prove that the total cost of the constructed backbone is within a small constant factor of the optimum for ho-mogeneous networks when either the nodes ’ costs are smooth or the network maximum node degree is bounded. We also show that with a small modification the constructed backbone is efficient for unicast: the total cost (or hop) of the least cost (or hop) path con-necting any two nodes using backbone is no more than 3 (or 4) times of the least cost (or hop) path in the original communication graph. As a side product, we give an efficient overlay based mul-ticast structure whose total cost is no more than 10 times of the minimum when the network is modeled by UDG. Our theoretical results are corroborated by our simulation studies.