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One of the research issues in wireless sensor networks (WSNs) is how to efficiently deploy sensors to cover an area. In this paper, we solve the k-coverage sensor deployment problem to achieve multi-level coverage of an area I. We consider two sub-problems: k-coverage placement and distributed dispatch problems. The placement problem asks how to determine the minimum number of sensors required and their locations in I to guarantee that I is k-covered and the network is connected; the dispatch problem asks how to schedule mobile sensors to move to the designated locations according to the result computed by the placement strategy such that the energy consumption due to movement is minimized. Our solutions to the placement problem consider both the binary and probabilistic sensing models, and allow an arbitrary relationship between the communication distance and sensing distance of sensors. For the dispatch problem, we propose a competition-based and a pattern-based schemes. The former allows mobile sensors to bid for their closest locations, while the latter allows sensors to derive the target locations on their own. Our proposed schemes are efficient in terms of the number of sensors required and are distributed in nature. Simulation results are presented to verify their effectiveness.