MWSR over an Uplink Gaussian Channel with Box Constraints: A Polymatroidal Approach

The rate capacity region of an uplink Gaussian channel is a generalized symmetric polymatroid. Practical applications impose additional lower and upper bounds on the rate allocations, which are represented by box constraints. A fundamental scheduling problem over an uplink Gaussian channel is to seek a rate allocation maximizing the weighted sum-rate (MWSR) subject to the box constraints. The best-known algorithm for this problem has time complexity O (n5 lnO(1) n). In this paper, we take a polymatroidal approach to developing a quadratic-time greedy algorithm and a linearithmic-time divide-and-conquer algorithm. A key ingredient of these two algorithms is a linear-time algorithm for minimizing the difference between a generalized symmetric rank function and a modular function after a linearithmic-time ordering.