Distributed wireless ad-hoc networks (DWANs) pose numerous technical challenges. Among them, two are widely considered as crucial: autonomous localized operation and minimization of energy consumption. We address the fundamental problem of how to maximize life-time of the network by using only local information while preserving network connectivity. We start by introducing the Care-Free Sleep (CS) Theorem that provides provably optimal necessary and sufficient conditions for a node to turn off

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... ts radio while ensuring that global connectivity is not affected. The CS theorem is the basis for an efficient localized algorithm that decides which node will turn its radio off, and for how long. The effectiveness of the approach is demonstrated using numerous simulations of the performance of the algorithm over a wide range of network parameters.