On Discrete Truthful Heterogeneous Two-Facility Location

We revisit the discrete heterogeneous two-facility location problem, in which there is a set of agents that occupy nodes of a line graph and have private approval preferences over two facilities. When the facilities are located at some nodes of the line, each agent suffers a cost that is equal to her total distance from the facilities she approves. The goal is to decide where to locate the two facilities so as to (a) incentivize the agents to truthfully report their preferences and (b) achieve a good approximation of the minimum total (social) cost or the maximum cost among all agents. For both objectives, we design deterministic strategyproof mechanisms with approximation ratios that significantly outperform the state of the art and complement these results with (almost) tight lower bounds.