In this paper, we present a localized Shortest-Path-Tree (SPT) based algorithm that copes 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, after which the total power consumption is further reduced by allowing each mobile node to search the replaceable links individually. The constructed topology ensures network connectivity, and possesses the following desirable energy-efficient features: (i) the power stretch factor is bounded and can be predetermined, (ii) the power consumption is evenly distributed among the mobile nodes, and (iii) the total power consumption is lower than that obtained by the best known algorithms. The performance improvements of the proposed algorithm are demonstrated through extensive simulations. We conclude our work with a discussion of future research directions toward more integrated mobile network architectures.
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