Facility Location with Public Locations and Private Doubly-Peaked Costs

TL;DR

This paper studies a facility location problem where agent locations are known but their preferred distances to facilities are private, introducing doubly-peaked costs, and provides bounds on approximation solutions in 1D and 2D settings.

Contribution

It re-examines facility location with known agent locations and private doubly-peaked costs, establishing bounds on approximation algorithms in 1D and 2D.

Findings

Established lower bounds on approximation ratios.

Developed upper bounds for specific cases.

Focused on 1D and 2D $L_1$ distance settings.

Abstract

In the facility location problem, the task is to place one or more facilities so as to minimize the sum of the agent costs for accessing their nearest facility. Heretofore, in the strategic version, agent locations have been assumed to be private, while their cost measures have been public and identical. For the most part, the cost measure has been the distance to the nearest facility. However, in multiple natural settings, such as placing a firehouse or a school, this modeling does not appear to be a good fit. For it seems natural that the agent locations would be known, but their costs might be private information. In addition, for these types of settings, agents may well want the nearest facility to be at the right distance: near, but not too near. This is captured by the doubly-peaked cost introduced by Filos-Ratsikas et al. (AAMAS 2017). In this paper, we re-examine the facility location problem from this perspective: known agent locations and private preferred distances to the nearest facility. We then give lower and upper bounds on achievable approximations, focusing on the problem in 1D, and in 2D with an $L_1$ distance measure.