We study a truthful two-facility location problem in which a set of agents have private positions on the line of real numbers and known approval preferences over two different facilities. Given the locations of the two facilities, the cost of an agent is the total distance from the facilities she approves. The goal is to decide where to place the facilities from a given finite set of candidate locations so as to (a) approximately optimize desired social objectives, and (b) incentivize the agents to truthfully report their private positions. We focus on the class of deterministic strategyproof mechanisms and show bounds on their approximation ratio in terms of the social cost (i.e., the total cost of the agents) and the max cost for several classes of instances depending on the preferences of the agents over the facilities.

翻译：我们研究了一个诚实双设施选址问题，其中一组代理在实数线上拥有私人位置，并对两个不同设施具有已知的批准偏好。给定两个设施的位置，代理的成本是其批准的设施的距离总和。目标是从给定的有限候选位置集合中决定设施的位置，以便（a）近似优化期望的社会目标，以及（b）激励代理如实报告其私人位置。我们聚焦于确定性策略证明机制类别，并根据代理对设施的偏好，针对若干实例类别展示了这些机制在社会成本（即代理的总成本）和最大成本方面的近似比界限。