On Truthful Constrained Heterogeneous Facility Location with Max-Variant Cost

TL;DR

This paper introduces a strategyproof mechanism for a facility location problem with agents having private positions and approval preferences, achieving significantly improved approximation bounds for minimizing total and maximum costs.

Contribution

It presents a novel mechanism that is both strategyproof and provides better approximation ratios than previous methods for the constrained heterogeneous facility location problem.

Findings

Achieves 11-approximation for total cost

Achieves 5-approximation for max cost

Improves previous bounds of 2n+1 and 9

Abstract

We consider a problem where agents have private positions on a line, and public approval preferences over two facilities, and their cost is the maximum distance from their approved facilities. The goal is to decide the facility locations to minimize the total and the max cost, while incentivizing the agents to be truthful. We design a strategyproof mechanism that is simultaneously $11$- and $5$-approximate for these two objective functions, thus improving the previously best-known bounds of $2n+1$ and $9$.