We consider the lifetime optimization problem for multicasting in wireless ad hoc networks, in which each node is equipped with a directional antenna and has limited energy supplies. Several distributed algorithms proposed recently are especially beneficial to a resource-constrained wireless ad hoc network. In this paper, we propose a new distributed algorithm and investigate its theoretical performance compared to existing distributed algorithms. We use a graph theoretic approach to obtain the

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... upper bound of the approximation ratio for a group of distributed algorithms. In particular, the derived upper bound in a closed form for each algorithm provides a sufficient condition to determine if the obtained solutions can reach optimum. Both theoretical and experimental performance analysis show that the new algorithm outperforms other proposals in terms of providing long-lived multicast tree. Index Terms-Wireless ad hoc network, approximation algorithm, multicast, directional antenna.