A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation
Computer Science and Game Theory
2020-06-30 v2 Data Structures and Algorithms
Abstract
We consider fair allocation of indivisible items under additive utilities. When the utilities can be negative, the existence and complexity of an allocation that satisfies Pareto optimality and proportionality up to one item (PROP1) is an open problem. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. We point out that the result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts.
Cite
@article{arxiv.1909.00740,
title = {A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation},
author = {Haris Aziz and Herve Moulin and Fedor Sandomirskiy},
journal= {arXiv preprint arXiv:1909.00740},
year = {2020}
}