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Mission-driven sensor networks usually have special lifetime requirements. However, the density of the sensors may not be large enough to satisfy the coverage requirement while meeting the lifetime constraint at the same time. Sometimes, coverage has to be traded for network lifetime. In this paper, we study how to schedule sensors to maximize their coverage during a specified network lifetime. Unlike sensor deployment, where the goal is to maximize the spatial coverage, our objective is to maximize the spatial-temporal coverage by scheduling sensors' activity after they have been deployed. Since the optimization problem is NP-hard, we first present a centralized heuristic whose approximation factor is proved to be 1/2, and then, propose a distributed parallel optimization protocol (POP). In POP, nodes optimize their schedules on their own but converge to local optimality without conflict with one another. Theoretical and simulation results show that POP substantially outperforms other schemes in terms of network lifetime, coverage redundancy, convergence time, and event detection probability.