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In this paper, we propose a k-coverage preserving protocol to achieve energy efficiency while ensuring the required coverage. In our protocol, we try to select a minimal active set of sensor nodes to reach energy conservation and maintain a complete area k-coverage. We model this problem as a minimum set cover problem and solve it by using a heuristic greedy algorithm. Based on the k-coverage preserving protocol, we then propose a protocol to deal with the probabilistic k-coverage requirement, in which each sensor could be assumed to be able to detect a nearby event with a certain probability. In the probabilistic k-coverage protocol, any point in the monitoring region can be sensed by at least k sensor nodes no lower than a confidence probability. Finally, we evaluate the performance of our protocols with simulations.