Fast centralized integer resource allocation algorithm and its distributed extension over digraphs

This paper studies the resource allocation problem with convex objective functions, subject to individual resource constraints, equality constraints, and integer constraints. The goal is to minimize the total cost when allocating the total resource D to n agents. We propose a novel min-heap and optimization relaxation based centralized algorithm and prove that it has a computational complexity of O(nlogn+nlogD) when the resource constraints of individual agents are [0, D], which outperforms the best known multi-phase algorithm with O(nlognlogD). By extending the centralized algorithm, we present a consensus based distributed optimization algorithm to solve the same problem. It is shown that the proposed distributed algorithm converges to a global minimizer provided that the digraph (representing the interaction topology of the agents) is strongly connected. All the updates used in the distributed algorithm rely only on local knowledge.