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Because of node mobility, mobile wireless networks experience rapid variations in the channel strengths, which could potentially be exploited for more cost-effective communications. The pioneering work by Grossglauser and Tse first demonstrated that a network under sufficient amount of random mobility can provide a larger scaling rate of capacity than a static network, at the cost of potentially unbounded end-to-end delay. Subsequent works have addressed the issue of the capacity gain under bounded delay. In this paper, we take a rather different approach in that we address the energy-efficient routing subject to the stringent packet delay and multiaccess interference constraints under the deterministic model. We incorporate the power control and scheduling in the routing decision and thus carry out cross-layer joint optimization. Our objective is to find the concurrent packets' relay paths associated with the exact relay instants, which can minimize the system-wide energy consumption at all nodes with the deterministic mobility pattern, traffic load, and channel conditions. We derive a dynamic programming algorithm to solve the optimization problem and also present an efficient polynomial time heuristic approach.