Power Controlled Scheduling with Consecutive Transmission Constraints: Complexity Analysis and Algorithm Design

We 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. We start by investigating the complexity of the problem and present the first NP-completeness proof in the literature. We propose a polynomial-time approximation algorithm, called guaranteed and greedy scheduling (GGS) algorithm, to tackle this problem. We 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, our algorithm together with its bounded approximation ratio is applicable even when the consecutive transmission constraint is relaxed. To the best of our knowledge, the proposed algorithm is the first known polynomial-time algorithm with a proven bounded approximation ratio for the joint power control and scheduling problem under the physical interference model. We further demonstrate the performance and advantages of our algorithm through extensive simulations.