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In this paper we study the minimum total energy and maximum network lifetime routing problem in wireless ad hoc networks. We develop competitive online schemes for an infinite sequence of random routing requests with provable approximation factors in both measures. In addition, we produce fundamental bounds on the expected total energy consumption and network lifetime in the optimal offline solution. Our results are verified through simulations. In the course of our analysis we derive an interesting property of shortest path trees (SPT) for a random point process. We show that the maximum edge length of any SPT is asymptotically equal to the maximum edge length of a minimum spanning tree. This result is of self interest for the study of energy efficient routing as many heuristics rely on SPTs.