## AbstractWe investigate the theoretical feasibility of near-optimal, distributed sleep scheduling in energy-constrained sensor networks with pairwise sensor redundancy. In this setting, an optimal sleep schedule is equivalent to an optimal fractional domatic partition of the associated redundancy graph. We present a set of realistic assumptions on the structure of the communication and redundancy relations; for the family of networks meeting these assumptions, we develop an efficient distributed approximation scheme for sleep scheduling. For any $\epsilon>0$, we demonstrate that it is possible to schedule the sensing activities of the nodes in a local and distributed manner so that the ratio of the optimum lifetime to the achieved lifetime of the network is at most $1+\epsilon$. The computational effort (time, memory and communication) required at each node depends on $\epsilon$ and the parameters of the network family, but given so-called anchor nodes (a set of nodes meeting certain density constraints) and locally unique node identifiers, the effort is independent of the actual network at hand; in particular, the required effort at each node remains constant as the size of the network is scaled up.
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