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One of most critical issues in power-constrained wireless sensor networks is to maximize the network lifetime. Recently, studies have been made on scheduling sensor activity to prolong network lifetime. In this paper, we address the maximum set covers (MSC) problem to maximize the network lifetime and propose an energy-efficient sensor scheduling algorithm for the MSC problem based on the branch and bound approach. Simulation results show that the proposed algorithms can contribute to extending the network lifetime and its performance is better than the existing greedy-based algorithm.