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.

翻译：我们首次研究在可加偏好下，采用并行算法在智能体间公平分配不可分割物品的问题。针对若干基础性问题，我们给出了高效的并行算法，包括在受限可加估值下寻找帕累托最优且EF1的分配方案、针对至多三个智能体寻找EF1分配方案，以及通过补贴实现无嫉妒分配。另一方面，我们证明快速并行算法不可能（形式上为$CC$-难）用于计算循环EF1分配方案。