On Discrete Truthful Heterogeneous Two-Facility Location

TL;DR

This paper studies a discrete two-facility location problem on a line, designing strategyproof mechanisms that incentivize truthful preferences while approximating optimal social costs and agent costs.

Contribution

It introduces new deterministic strategyproof mechanisms with improved approximation ratios and provides tight lower bounds for the discrete heterogeneous two-facility location problem.

Findings

Mechanisms outperform previous state-of-the-art in approximation ratios.

Provides tight lower bounds for the problem.

Achieves incentive compatibility with good cost approximations.

Abstract

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 derives 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.