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The coverage problem in sensor networks studies how to turn redundant sensors off while maintaining a required level of coverage. The existing algorithms and protocols are proven to be effective to conserve energy and prolong network lifetime, but only support a static level of sensing coverage. In contrast, many sensor network applications may require a dynamic level of coverage, which changes from area to area and from time to time. To this end, new algorithms must be designed. In this paper, we propose to adapt the sensing scheduling of sensor nodes to the dynamic level of coverage. In the proposed scheme, the lifetime of a sensor node is divided into epochs. At each epoch, the base station computes a minimum set of active nodes based on the current level of coverage requirement. Each sensor samples the field only if it is determined by the base station to sense. The problem of selecting a minimum set of active sensor nodes for a required level of sensing coverage is formulated as an integer programming problem and a heuristic algorithm is proposed. The algorithm is shown to have an approximation factor close to 2 In n. The scheme eliminates redundant sensing by adapting the sensing scheduling to the dynamic sensing coverage requirement at each epoch. The simulation results show that the proposed scheme can extend the network lifetime significantly, in comparison with existing schemes for static sensing scheduling when the coverage load is low on the field.