分布式设施选址失真的解决
Settling the Distortion of Distributed Facility Location
摘要：
我们研究了分布式设施选址问题，其中一组位置在实数线上的代理被划分为不相交的区域，目标是选择一个点来满足一定的标准，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为两个步骤：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：不受限制的机制，假设代理人直接提供他们的真实位置作为输入，和策略保护机制，处理战略代理人，旨在激励他们如实报告自己的立场。对于这两个类，我们展示了严格的界限上的最佳近似的几个最小化的社会目标，包括众所周知的社会成本（总距离的代理从选择点）和最大成本（所有代理从选择点之间的最大距离），以及其他公平启发的目标是量身定制的分布式设置。
英文摘要：
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 social cost (total distance of agents from chosen point) and max cost (maximum distance among all agents from chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting.
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