Abstract Minimizing the energy consumption of target tracking using a mobile sensor network is proved to be NPcomplete. Based on proximity graph, an approximately optimal solution named distributed leader-follower strategy is presented. Nodes close to the target predicted location lead faraway nodes to cover the probable region where the target may exist next time. Meanwhile, the overall network connectivity can be maintained. We have proved that the energy consumption of the nodes moving under the control of the algorithm is within a constant factor of the optimal result. Simulation has been conducted to demonstrate the performance of the algorithm. Key words Mobile sensor network, NP-complete, proximity graph, network connectivity 1 , , , . [1∼3] , . , . , , . . 2006-10-23 2007-2-2 Received October 23, 2006; in revised form February 2, 2007 (60334010, 60475029), Supported by National Natural Science Foundation of China (60334010, 60475029), Microsoft-CUHK Joint Laboratory for Human...