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Wireless Sensor Networks are emerging as a key sensing technology, with diverse military and civilian applications. In these networks, a large number of sensors perform distributed sensing of a target field. Each sensor is a small battery-operated device that can sense events of interest in its sensing range and can communicate with neighboring sensors. A sensor cover is a subset of the set of all sensors such that every point in the target field is in the interior of the sensing ranges of at least different sensors in the subset, where k is a given positive integer. The lifetime of the network is the time from the point the network starts operation until the set of all sensors with non-zero remaining energy does not constitute a sensor cover. 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 …