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Many applications require k-coverage network to ensure the quality of the monitored area. Meanwhile, preserving the required k-coverage for the maximum network lifetime with a small computation cost is a major challenge. In this paper, we propose Maximum Layers Scheduling algorithm (MLS) to preserve the k-coverage and prolong the network lifetime. MLS efficiently builds and schedules a maximum number of layers in which each layer is 1-covered and 1- connected. MLS efficiently reduces the computation complexity, where sensors only trace intersection points of a small number of sensing neighbors in the layer. Experimental results show that the MLS algorithm minimizes the average number of active sensors, and the average coverage degree compared to two popular k-coverage algorithms and prolongs the network lifetime.