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Wireless sensor networks have emerged recently as an effective way of gathering useful information from areas of interest. Prolonging the network lifetime has become the primary concern in data gathering due to the limited battery power of sensors. An underlying assumption of most existing work is that all the sensors are working simultaneously during the whole process of data gathering. In this paper, we introduce a new definition of the network lifetime in view of the coverage condition, and then investigate the coverage-based maximum lifetime data gathering problem theoretically. Two critical issues are how to selectively organize part of sensors to work and how to execute routing in a single working set. Considering both of these two problems together, we propose the algorithm CODAG. CODAG employs the tree structured routing scheme and enables the routing effects of two different sets theoretically comparable. Based on the maximal increased weight in the routing tree, it divides all the sensors into disjoint cover sets without redundant ones, which in turn leads to the better routing effect. Experimental results show that our algorithm has the good performance for prolonging the lifetime of the whole sensor network.