PROPm Allocations of Indivisible Goods to Multiple Agents
This solves a foundational problem in fair division for multi-agent systems, with broad implications in economics and computer science.
The paper tackled the problem of guaranteeing a fair allocation of indivisible goods among any number of agents using the PROPm fairness notion, proving that such an allocation always exists and providing a polynomial-time algorithm to compute it.
We study the classic problem of fairly allocating a set of indivisible goods among a group of agents, and focus on the notion of approximate proportionality known as PROPm. Prior work showed that there exists an allocation that satisfies this notion of fairness for instances involving up to five agents, but fell short of proving that this is true in general. We extend this result to show that a PROPm allocation is guaranteed to exist for all instances, independent of the number of agents or goods. Our proof is constructive, providing an algorithm that computes such an allocation and, unlike prior work, the running time of this algorithm is polynomial in both the number of agents and the number of goods.