  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.
