Minimum-Energy Broadcasting in Static Ad Hoc Wireless Networks

Energy conservation is a critical issue in ad hoc wireless networks for node and network life since the nodes are powered by batteries only One major approach for energy conservation is to route a communica tion session along the route which requires the lowest total energy con sumption This optimization problem is referred to as Minimum Energy Routing While the minimum energy unicast routing problem can be solved in polynomial time by shortest path algorithms it remains open whether the minimum energy broadcast routing problem can be solved in polynomial time despite the NP hardness of its general graph version Re cently three greedy heuristics were proposed in MST minimum span ning tree SPT shortest path tree and BIP broadcasting incremental power They evaluated their approaches through simulations but lit tle is known about their analytical performance The main contribution of this paper is a quantitative characterization of their performances in terms of approximation ratios By exploring geometric structures of Eu clidean MSTs we were able to prove that the approximation ratio of MST is between and and the approximation ratio of BIP is between and On the other hand we show that the approximation ratio of SPT is at least n where n is the number of receiving nodes To the best of our knowledge these are the rst analytical results for the minimum energy broadcasting problem