An Improved Approximation Algorithm for the Minimum Energy Consumption Broadcast Subgraph

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In an ad-hoc wireless network each station has the capacity of modifying the area of coverage with its transmission power. Controlling the emitted transmission power allows to significantly reduce the energy consumption and so to increase the lifetime of the network. In this paper we focus on the Minimum Energy Consumption Broadcast Subgraph (MECBS) problem [1,2,6], whose objective is that of assigning a transmission power to each station in such a way that a message from a source station can be forwarded to all the other stations in the network with a minimum overall energy consumption. The MECBS problem has been proved to be inapproximable within (1–ε) ln n unless NPDTIME(n O(log log n)) [2,6], where n is the number of stations. In this work we propose a 2H n − − 1-approximation greedy algorithm which, despite its simplicity, improves upon the only previously known ratio of 10.8 ln n [1] and considerably approaches the best-known lower bound on the approximation ratio.