We study the distributed facility location problem, where a set of agents with positions on the line of real numbers are partitioned into disjoint districts, and the goal is to choose a point to satisfy certain criteria, such as optimize an objective function or avoid strategic behavior. A mechanism in our distributed setting works in two steps: For each district it chooses a point that is representative of the positions reported by the agents in the district, and then decides one of these representative points as the final output. We consider two classes of mechanisms: Unrestricted mechanisms which assume that the agents directly provide their true positions as input, and strategyproof mechanisms which deal with strategic agents and aim to incentivize them to truthfully report their positions. For both classes, we show tight bounds on the best possible approximation in terms of several minimization social objectives, including the well-known average social cost (average total distance of agents from the chosen point) and max cost (maximum distance among all agents from the chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting, in particular, the max-of-average and the average-of-max.

我们研究分布式设施选址问题，其中一组位置位于实数线上的智能体被划分为不相交的区域，目标是选择一个点来满足某些标准，例如优化目标函数或避免策略行为。我们的分布式设置中的机制分两步工作：对于每个地区，它选择一个代表该地区代理报告的位置的点，然后决定这些代表点之一作为最终输出。我们考虑两类机制：无限制机制，假设代理直接提供其真实位置作为输入；策略证明机制，处理策略代理并旨在激励他们如实报告其位置。对于这两个类别，我们在几个最小化社会目标方面显示了最佳近似值的严格界限，包括众所周知的平均社会成本（智能体与所选点的平均总距离）和最大成本（来自所选点的所有智能体之间的最大距离）选定的点），以及其他为分布式设置量身定制的公平目标，特别是最大平均数和最大平均数。