For a multihop sensor network with n sensors, this paper presents an O(n) distributed greedy algorithm for extracting a rooted spanning tree to improve the lifetime of the overall network. It spontaneously determines a data gathering schedule from the sensors towards the base station (the root). No global knowledge about the topology is required for the computation and also each sensor does not need to access the base station directly. Simulation studies show that in terms of system lifetime, the proposed algorithm significantly outperforms the scheduling based on the Minimum Spanning Tree (MST), or the Shortest Path (SP) routing techniques. Performance comparison with PEGASIS [7] shows that the proposed algorithm performs better as more and more nodes die out.