Fairly Allocating Goods in Parallel

09/15/2023

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by   Rohan Garg, et al.

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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.