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In the process of fulfilling k-coverage over target nodes, a large quantity of redundant data may be produced, which will cause network congestion, reduce communication efficiency, impair coverage quality, and exhaust network energy quickly. To solve this problem, the paper proposes an Energy-Efficient k-Coverage Algorithm (EEKCA), which attempts to construct a network coverage model by utilizing the relative positions of nodes. Through analyzing the model, the coverage expectations for nodes in the monitored area and the minimum number of nodes required for full coverage are computed. As for power consumption, the paper presents an energy shifting function between working nodes and neighboring nodes, by use of which the scheduling for low-energy node is completed, balancing the energy consumption over the entire network and optimizing network resources. Finally, simulation results suggest that the proposed algorithm not only can improve the coverage quality of network but also can prevent the rapid depletion of node energy, thus achieving the goal of extending network lifetime. [ABSTRACT FROM AUTHOR]