A faster algorithm for the resource allocation problem with convex cost functions

Cong Shi, Huanan Zhang, Chao Qin

Abstract: We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a wide variety of applications. In this paper, we propose a novel polynomial-time divide-and-conquer algorithm (called the multi-phase algorithm) and prove that it has a computational complexity of O(n log(n) log(N)), which outperforms the best known polynomial-time algorithm with O(n (log(N))^2).