This work proposes a distributed algorithm for energy optimal routing in a wireless sensor network. The routing problem is described as a mathematical problem by the minimum-cost multi-commodity network flow problem. Due to the separability of the problem, we use the duality theorem to derive the distributed algorithm. The algorithm computes the energy optimal routing in the network without any central node or knowledge of the whole network structure. Each node only needs to know the flow which is supposed to send or receive and the costs and capacities of the neighboring links. An evaluation of the presented algorithm on benchmarks for the energy optimal data flow routing in sensor networks with up to 100 nodes is presented.
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