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