# On Discrete Truthful Heterogeneous Two-Facility Location

arXiv: https://arxiv.org/abs/2109.04234 · HTML: https://mlsanity.com/paper/2109.04234/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2021.

## Built on by (most cited first, 2 of 2)

- [Equilibria in Two-Stage Facility Location with Atomic Clients](https://mlsanity.com/paper/2403.03114/) (2024)
- [Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model](https://mlsanity.com/paper/2204.11282/) (2022)

## Abstract (arXiv)

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.