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A sensor network of nodes with wireless transceiver capabilities and limited energy is considered. We propose distributed algorithms to compute an optimal routing scheme that maximizes the time at which the first node in the network drains out of energy. The problem is formulated as a linear programming problem and subgradient algorithms are used to solve it in a distributed manner. The resulting algorithms have low computational complexity and are guaranteed to converge to an optimal routing scheme that maximizes the network lifetime. The algorithms are illustrated by an example in which an optimal flow is computed for a network of randomly distributed nodes.