We consider ad-hoc wireless networks and the topology control problem defined as minimizing the amount of power needed to maintain connectivity. The issue boils down to selecting the optimum transmission power level at each node based on the position information of reachable nodes. Local decisions regarding the transmission power level induce a subgraph of the maximum powered graph Gmax in which edges represent direct reachability at maximum power. In this paper we propose an analysis for constructing minimum-energy path-preserving subgraphs of Gmax, i.e. subgraphs minimizing the energy consumption between node pairs. We also propose an algorithm for constructing subgraph of Gmax based on one-hop neighbor information. By presenting experimental results we show the effectiveness of our proposed algorithm.
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