Abstract-In this paper we study a joint transmission scheduling and power control problem that arises in wireless networks. The goal is to assign time slots (or channels) and transmitting powers to communication links such that all communication requests are processed correctly, specified Quality-of-Service (QoS) requirements are met, and the number of required time slots is minimized. The first main result proves that the problem, also known as the wireless scheduling problem, is NP-hard. We then solve a mixed-integer linear programming (MILP) formulation of the problem with Branch & Bound (B&B) and Cutting Plane (CP) approaches. We enhance the computational performance of these schemes with heuristic procedures that provide tighter upper and lower bounds. We close with an extensive computational study, which shows that despite the complexity of the problem, the proposed methodology scales to problems of nontrivial size. Our algorithms can therefore serve as a benchmark for the performance evaluation of heuristic or distributed algorithms that aim to find near-optimal solutions without information about the whole network.
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