Allocating Chores with Restricted Additive Costs: Achieving EFX, MMS, and Efficiency Simultaneously

TL;DR

This paper introduces a novel allocation algorithm for chores with restricted additive costs, achieving fairness (EFX, MMS) and efficiency simultaneously, with proven optimal approximation ratios.

Contribution

It presents the first algorithm that guarantees both EFX and MMS fairness for chores with restricted additive costs, while also approximating social cost optimally.

Findings

Algorithm computes EFX and MMS allocations.

Achieves a 2-approximation of optimal social cost.

Approximation ratio is proven to be optimal.

Abstract

In a web-based review platform, papers from various research fields must be assigned to a group of reviewers. Each paper has an inherent cost, which represents the effort required for reading and evaluating it (e.g., the paper's length). Reviewers can bid on papers they are interested in, and if they are assigned a paper they have bid on, no cost is incurred. Otherwise, the inherent cost $c(e)$ for paper $e$ applies. We capture this with a model of restricted additive costs: every item $e$ has a cost $c(e)$, and each agent either incurs $0$ or $c(e)$ for $e$. In this work, we study how to allocate such chores fairly and efficiently. We propose an algorithm for computing allocations that are both EFX and MMS. Furthermore, we show that our algorithm achieves a $2$-approximation of the optimal social cost, and the approximation ratio is optimal. We also show that slightly weaker fairness guarantees can be obtained if one requires the algorithm to run in polynomial time.