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In wireless sensor networks (WSNs), a large number of sensors perform distributed sensing of a target field. A sensor cover is a subset of the set of all sensors that covers the target field. The lifetime of the network is the time from the point the network starts operation until the set of all sensors with nonzero remaining energy does not constitute a sensor cover any more. An important goal in sensor networks is to design a schedule-that is, a sequence of sensor covers to activate in every time slot-so as to maximize the lifetime of the network. In this paper, we design a polynomial-time distributed algorithm for maximizing the lifetime of the network and prove that its lifetime is at most a factor O(logn * lognB) lower than the maximum possible lifetime, where n is the number of sensors and B is an upper bound on the initial energy of each sensor. Our algorithm does not require knowledge of the locations of nodes or directional information, which is difficult to obtain in sensor networks. Each sensor only needs to know the distances between adjacent nodes in its transmission range and their sensing radii. In every slot, the algorithm first assigns a weight to each node that is exponential in the fraction of its initial energy that has been used up so far. Then, in a distributed manner, it finds an O(logn) approximate minimum weight sensor cover, which it activates in the slot.