Distributed Agent-Constrained Truthful Facility Location

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.