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This paper presents a localized shortest-path-tree (SPT) based algorithm to cope with the topology control problem in wireless ad hoc networks. Each mobile node determines its own transmission power based only on its local information. The proposed algorithm first constructs local SPTs from the initial graph, and then the total power consumption is further reduced by allowing each mobile node to search and excise the replaceable links individually. The constructed topology ensures network connectivity, and possesses several desirable energy-efficient features: 1) its power stretch factor is bounded and can be predetermined, 2) the power consumption is evenly distributed among the mobile nodes, and 3) its total power consumption is lower than that obtained from the best known algorithms. The performance improvements of the proposed algorithm are demonstrated through extensive simulations.