Facility Reallocation on the Line

Facility Reallocation on the Line

Bart de Keijzer, Dominik Wojtczak

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Main track. Pages 188-194. https://doi.org/10.24963/ijcai.2018/26

We consider a multi-stage facility reallocation problems on the real line, where a facility is being moved between stages based on the locations reported by n agents. The aim of the reallocation mechanism is to minimize the social cost, i.e., the sum over the total distance between the facility and all agents at all stages, plus the cost incurred for moving the facility. We also study this problem both in the offline setting and online setting. In the offline case the mechanism has full knowledge of the agent locations in all future stages, and in the online setting the mechanism does not know these future locations and must decide the location of the facility on a stage-per-stage basis. For both cases, we derive the optimal mechanism, where for the online setting we show that its competitive ratio is (n+2)/(n+1). As neither of these mechanisms turns out to be strategyproof, we propose another strategyproof mechanism which has a competitive ratio of (n+3)/(n+1) for odd n and (n+4)/n for even n, which we conjecture to be the best possible. We also consider a generalization with multiple facilities and weighted agents, for which we show that the optimum can be computed in polynomial time for a fixed number of facilities.
Keywords:
Agent-based and Multi-agent Systems: Agent Theories and Models
Agent-based and Multi-agent Systems: Noncooperative Games
Agent-based and Multi-agent Systems: Algorithmic Game Theory
Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems
Agent-based and Multi-agent Systems: Computational Social Choice