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In this paper, given a random distribution of sensor nodes, we pose the problem of finding maximum number of connected set covers such that each set can guarantee the required coverage of the region of interest. It requires just a one-time computation during initialization. Once the connected set covers are known, the sets may remain active in a round robin fashion to cover the region enhancing the life time of the network significantly. Firstly, two centralized greedy algorithms have been proposed to solve the problem from two different view points. But since centralized algorithms are not suitable for large self-organized sensor networks, a localized algorithm has been proposed finally that uses only local information at individual nodes to find a solution. Simulation studies show that these algorithms can enhance the network lifetime manifold, and most interestingly the performance of the distributed algorithm is comparable with the centralized ones in terms of number of partitions though it requires much less computation and communication overhead.