An Algorithmic Framework for Approximating Maximin Share Allocation of Chores

TL;DR

This paper introduces a new algorithmic approach to fairly divide indivisible chores among agents, achieving a better approximation ratio for maximin share fairness than previous methods.

Contribution

The paper presents a novel algorithm that improves the approximation ratio for maximin share allocation of chores from 4/3 to 11/9.

Findings

Achieves an 11/9 approximation ratio for maximin share allocation.

Establishes connections between fair division and job scheduling problems.

Discusses efficiency improvements for the proposed algorithm.

Abstract

In this paper, we consider the problem of how to fairly dividing $m$ indivisible chores among $n$ agents. The fairness measure we considered here is the maximin share. The previous best known result is that there always exists a $\frac{4}{3}$ approximation maximin share allocation. With a novel algorithm, we can always find a $\frac{11}{9}$ approximation maximin share allocation for any instances. We also discuss how to improve the efficiency of the algorithm and its connection to the job scheduling problem.