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Throughput-optimal multihop wireless network operation entails a key physical-layer optimization problem: maximizing a weighted sum of link rates, with weights given by the differential queue backlogs. This emerges in joint back-pressure routing and power control, which is central in cross-layer wireless networking. We begin by showing that the core problem is not only nonconvex, but also NP-hard. This is a negative result, which however comes with a positive flip side: drawing from related developments in the digital subscriber line (DSL) literature, we propose effective ways to approximate it. Exploiting quasi-periodicity of the power allocation in stable setups due to the push-pull nature of the solution, we derive two custom algorithms that offer excellent throughput performance at reasonable, worst-case polynomial complexity. Judicious simulations illustrate the merits of the proposed algorithms.
Date of Publication: April 2012