On Approximation Ratios of Minimum-Energy Multicast Routing in Wireless Networks

In the broadcasting of ad hoc wireless networks, energy conservation is a critical issue. Three heuristic algorithms were proposed in Wieselthier et al.(2001) for finding approximate minimum-energy broadcast routings: MST(minimum spanning tree), SPT(shortest-path tree), and BIP(broadcasting incremental power). Wan et al.(2001) characterized their performance in terms of approximation ratios. This paper points out some mistakes in the result of Wan et al.(2001), and proves that the upper bound of sum of squares of lengths of the edges in Euclidean MST in unit disk can be improved to 10.86, thus improves the approximation ratios of MST and BIP algorithm.Supported by Natural Science Foundation of China (60223004, 603210022)