Abstract
Motivated by the fair rate allocation in a multiaccess Gaussian channel, this paper studies the problem of fair rate allocation over a generalized symmetric polymatroid with box constraints. The best-known algorithm for this problem has time complexity $\mathcal{O} (n^{5}\, \ln^{\mathcal{O}(1)\, } n)$. In this paper, we present a divide-and-conquer algorithm for this problem with quadratic running time. It is an implementation of a refined decomposing method for the more general separate concave maximization over a polymatroid with box constraints. A key ingredient of the algorithm is a linear-time algorithm for a generalized knapsack problem.
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