Minimum-Energy Broadcast Routing in Static Ad Hoc Wireless Networks

Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite of the NP-hardness of its general graph version. Recently three greedy heuristics were proposed in [8]: MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in [8], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we have been able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between 13 3 and 12. On the other hand, the approximation ratio of SPT is shown to be at least n2 , where n is the number of receiving nodes. To our best knowledge, these are the first analytical results for minimum-energy broadcasting.