Facility location problems often permit facilities to be located at any position. But what if this is not the case in practice? What if facilities can only be located at particular locations like a highway exit or close to a bus stop? We consider here the impact of such constraints on the location of facilities on the performance of strategy proof mechanisms for locating facilities.We study four different performance objectives: the total distance agents must travel to their closest facility, the maximum distance any agent must travel to their closest facility, and the utilitarian and egalitarian welfare.We show that constraining facilities to a limited set of locations makes all four objectives harder to approximate in general.

中文翻译：

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有限地点设施选址的策略证明机制

设施位置问题通常允许设施位于任何位置。但如果实际情况并非如此呢？如果设施只能位于特定位置（例如高速公路出口或靠近公交车站）怎么办？我们在此考虑这种对设施位置的约束对设施定位策略证明机制性能的影响。我们研究了四个不同的性能目标：代理必须到达最近设施的总距离，任何代理必须到达的最大距离他们最近的设施，以及功利主义和平等主义的福利。我们表明，将设施限制在一组有限的位置会使所有四个目标在一般情况下更难接近。