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Many efforts have been made for addressing coverage problems in sensor networks. They fall into two categories, full coverage and barrier coverage, featured as static coverage. In this work, we study a new coverage scenario, sweep coverage, which differs with the previous static coverage. In sweep coverage, we only need to monitor certain points of interest (POIs) periodically so the coverage at each POI is time-variant, and thus we are able to utilize a small number of mobile sensors to achieve sweep coverage among a much larger number of POIs. We investigate the definitions and model for sweep coverage. Given a set of POIs and their sweep period requirements, we prove that determining the minimum number of required sensors (min-sensor sweep-coverage problem) is NP-hard, and it cannot be approximated within a factor of 2. We propose a centralized algorithm with constant approximation ratio 3 for the min-sensor sweep-coverage problem. We further characterize the nonlocality of the problem and design a distributed sweep algorithm, DSWEEP, cooperating sensors to provide efficiency with the best effort. We conduct extensive simulations to study the performance of the proposed algorithms. Our simulations show that DSWEEP outperforms the randomized scheme in both effectiveness and efficiency.