We consider a truthful facility location problem in which there is a set of agents with private locations on the line of real numbers, and the goal is to place a number of facilities at different locations chosen from the set of those reported by the agents. Given a feasible solution, each agent suffers an individual cost that is either its total distance to all facilities (sum-variant) or its distance to the farthest facility (max-variant). For both variants, we show tight bounds on the approximation ratio of strategyproof mechanisms in terms of the social cost, the total individual cost of the agents.

翻译：我们考虑一个真实的设施选址问题，其中有一组代理，其私有位置位于实数轴上，目标是从代理报告的位置集合中选择不同位置来放置若干设施。给定一个可行解，每个代理承受的个体成本要么是其到所有设施的总距离（求和变体），要么是其到最远设施的距离（最大变体）。对于这两种变体，我们证明了策略证明机制在社会成本（代理的个体成本总和）方面的近似比紧界。