Fairly Allocating Goods in Parallel

TL;DR

This paper develops fast parallel algorithms for fair division of indivisible goods among agents, addressing problems like EF1 and Pareto optimality, while also proving certain fairness computations are computationally hard.

Contribution

It introduces new efficient parallel algorithms for key fair division problems and establishes hardness results for others.

Findings

Fast parallel algorithms for Pareto optimal and EF1 allocations under certain valuations.

Efficient algorithms for EF1 allocations with up to three agents.

Hardness results showing no fast parallel algorithms for Round-Robin EF1 allocations.

Abstract

We initiate the study of parallel algorithms for fairly allocating indivisible goods among agents with additive preferences. We give fast parallel algorithms for various fundamental problems, such as finding a Pareto Optimal and EF1 allocation under restricted additive valuations, finding an EF1 allocation for up to three agents, and finding an envy-free allocation with subsidies. On the flip side, we show that fast parallel algorithms are unlikely to exist (formally, $CC$-hard) for the problem of computing Round-Robin EF1 allocations.