Settling the Distortion of Distributed Facility Location

TL;DR

This paper investigates distributed facility location mechanisms on a line, establishing tight bounds for approximation ratios under both unrestricted and strategyproof settings for various social objectives.

Contribution

It introduces a formal model for distributed facility location with strategic agents and derives tight bounds for mechanism performance across different objectives.

Findings

Tight bounds for approximation ratios in distributed setting

Analysis of strategyproof mechanisms for strategic agents

Comparison of social cost and max cost objectives

Abstract

We study the distributed facility location problem, where a set of agents with positions on the line of real numbers are partitioned into disjoint districts, and the goal is to choose a point to satisfy certain criteria, such as optimize an objective function or avoid strategic behavior. A mechanism in our distributed setting works in two steps: For each district it chooses a point that is representative of the positions reported by the agents in the district, and then decides one of these representative points as the final output. We consider two classes of mechanisms: Unrestricted mechanisms which assume that the agents directly provide their true positions as input, and strategyproof mechanisms which deal with strategic agents and aim to incentivize them to truthfully report their positions. For both classes, we show tight bounds on the best possible approximation in terms of several minimization social objectives, including the well-known social cost (total distance of agents from chosen point) and max cost (maximum distance among all agents from chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting.