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The authors study the joint power control and minimum-frame-length scheduling problem in wireless networks, under the physical interference model and subject to consecutive transmission constraints. They start by investigating the complexity of the problem and present the first NP-completeness proof in the literature. They propose a polynomial-time approximation algorithm, called Guaranteed and Greedy Scheduling (GGS) algorithm, to tackle this problem. They prove a bounded approximation ratio of the proposed algorithm relative to the optimal scheduling algorithm. Moreover, the proposed algorithm significantly outperforms the state-of-the-art related algorithm. Interestingly, their algorithm together with its bounded approximation ratio is applicable even when the consecutive transmission constraint is relaxed.
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