Approximation Algorithms for Power-Aware Scheduling of Wireless Sensor Networks with Rate and Duty-Cycle Constraints

We develop algorithms for finding the minimum energy transmission schedule for duty-cycle and rate constrained wireless sensor nodes transmitting over an interference channel. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the non-convex constraints, we develop fully polynomial approximation schemes (FPAS) for finding optimal schedules by considering restricted versions of the problem using multiple discrete power levels. We first show a simple dynamic programming solution that optimally solves the restricted problem. For two fixed transmit power levels (0 and P ), we then develop a 2-factor approximation for finding the optimal fixed transmission power level per time slot, Popt, that generates the optimal (minimum) energy schedule. This can then be used to develop a (2, 1 + )-FPAS that approximates the optimal power consumption and rate constraints to within factors of 2 and arbitrarily small > 0, respectively. Finally, we develop an algorithm for computing the optimal number of discrete power levels per time slot (O(1/ )), and use this to design a (1, 1 + )-FPAS that consumes less energy than the optimal while violating each rate constraint by at most a 1 + factor.