Distributed Agent-Constrained Truthful Facility Location

2026-01-21

AI Summary

This study addresses the distributed facility location problem under group constraints, wherein each fixed group first selects a representative, and then k facility locations are chosen from among these representatives to minimize social cost—defined either as the total distance (sum-variant) or the maximum distance (max-variant). Within this two-stage framework, the work proposes the first strategyproof mechanism and rigorously analyzes its approximation performance by integrating tools from mechanism design, game theory, and approximation algorithms. Tight theoretical bounds on the approximation ratios are established for both individual cost models, thereby filling a critical gap in the literature concerning strategyproof mechanism design for this class of problems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study a distributed facility location problem in which a set of agents, each with a private position on the real line, is partitioned into a collection of fixed, disjoint groups. The goal is to open $k$ facilities at locations chosen from the set of positions reported by the agents. This decision is made by mechanisms that operate in two phases. In Phase 1, each group selects the position of one of its agents to serve as the group's representative location. In Phase 2, $k$ representatives are chosen as facility locations. Once the facility locations are determined, each agent incurs an individual cost, defined either as the sum of its distances to all facilities (sum-variant) or as the distance to its farthest facility (max-variant). We focus on the class of strategyproof mechanisms, which preclude the agents from benefiting through strategic misreporting, and establish tight bounds on the approximation ratio with respect to the social cost (the total individual agent cost) in both variants.

Problem

• distributed facility location
• strategyproof mechanism
• social cost
• agent groups
• truthful reporting

Innovation

• distributed facility location
• strategyproof mechanism
• group representation
• approximation ratio
• truthful mechanism