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We address the problem of locating facilities on the $[0,1]$ interval basedon reports from strategic agents. The cost of each agent is her distance to theclosest facility, and the global objective is to minimize either the maximumcost of an agent or the social cost.  As opposed to the extensive literature on facility location which considersthe multiplicative error, we focus on minimizing the worst-case additive error.Minimizing the additive error incentivizes mechanisms to adapt to the size ofthe instance. I.e., mechanisms can sacrifice little efficiency in smallinstances (location profiles in which all agents are relatively close to oneanother), in order to gain more [absolute] efficiency in large instances. Weargue that this measure is better suited for many manifestations of thefacility location problem in various domains.  We present tight bounds for mechanisms locating a single facility in bothdeterministic and randomized cases. We further provide several extensions forlocating multiple facilities.

Truthful Facility Location with Additive Errors