Global Optimal Routing, Scheduling and Power Control for Multi-Hop Wireless Networks with Interference

We consider the problem of joint routing, scheduling and power control in multi-hop wireless networks. We use a linear relation between link capacity and signal to interference noise ratio in our formulation. In a previous work, using a duality approach, the optimal link scheduling and power control that minimizes the total average transmission power is found. We formulate this problem as a linear programming problem with exponential number of constraints. To cope with the exponential number of constraints, we propose an iterative algorithm based on the cutting plane method. The separation oracle for the cutting plane algorithm turns out to be an element-wise concave optimization problem that can be effectively solved using branch and bound algorithm. We extend the same method to find the optimal routing scheduling and power control. Simulation results show that this methodology is more efficient and scalable compare to the previously proposed algorithm.