Given a multihop wireless network and a source-destination pair of nodes, this paper addresses the problem of jointly selecting a communication route and allocating transmit power levels, so that the end-to-end spectral efficiency of the route exceeds a desired threshold and the maximum power used by any link is minimized. Spectral-efficient routing has been subject to interest in the recent literature. The transmit power level, however, has been assumed to be known, and route selection was considered in isolation. This paper presents the first polynomial-time algorithm for joint spectral-efficient routing and power allocation that provides solutions arbitrarily close to the optimal one. Our computational results further illustrate the efficiency of the proposed approach.
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