Optimum integrated link scheduling and power control for ad hoc wireless networks

In this paper, we develop a new mathematical programming formulation for minimizing the schedule length in ad hoc wireless networks based on the optimal joint scheduling of transmissions across the multi-access communication links and allocation of transmit power levels, while meeting the requirements on the signal-to-interference and noise ratio (SINR) at intended receivers. We prove that the problem can be represented as a mixed integer linear programming (MILP) and show that the latter yields a solution that consists of transmit power levels that are strongly Pareto optimal. We demonstrate that our MILP formulation can be used effectively to derive optimal scheduling and power levels for networks with as many as 30 designated communication links. We exhibit that the MILP formulation can be also effectively solved to provide tight upper and lower bounds (corresponding to an approximation factor Δ) for the optimum schedule length of networks with as many as 100 designated links. We prove that the integrated link scheduling and power control problem is NP-complete. Consequently, we develop and investigate a heuristic algorithm of polynomial complexity (O|LO|⁵) for solving the problem in a timely and practical manner. Our algorithm is based on the properties of a novel interference graph (the power-based interference graph) that we have introduced. We demonstrate that the frame length of schedules realized by our heuristic schemes reside in the 25 percentile of those attained by the optimal mechanism for randomly generated topologies.