  We initiate the study of the heterogeneous facility location problem with
limited resources. We mainly focus on the fundamental case where a set of
agents are positioned in the line segment [0,1] and have approval preferences
over two available facilities. A mechanism takes as input the positions and the
preferences of the agents, and chooses to locate a single facility based on
this information. We study mechanisms that aim to maximize the social welfare
(the total utility the agents derive from facilities they approve), under the
constraint of incentivizing the agents to truthfully report their positions and
preferences. We consider three different settings depending on the level of
agent-related information that is public or private. For each setting, we
design deterministic and randomized strategyproof mechanisms that achieve a
good approximation of the optimal social welfare, and complement these with
nearly-tight impossibility results.
