Facility Location Games on the Time Horizon

Abstract

We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a transient agent stays for a number of consecutive stages and needs to be served by the facility in one of the stages. The facility at different stages can be in different locations. In the first model, we assume there is no cost for moving the facility across the stages. We focus on optimal algorithms to minimize both the social cost objective, defined as the total distance of all agents to the facility over all stages, and the maximum cost objective, defined as the max distance of any agent to the facility over all stages. For each objective, we give an XP algorithm, i.e., solvable in nf(k) for some fixed parameter k and computable function f, and show that there is a polynomial-time algorithm when a natural first-come-first-serve (FCFS) order of serving is enforced. We then consider the mechanism design problem where the agents' locations are private and design a group strategy-proof mechanism that achieves good approximation ratios for both objectives and settings with and without FCFS ordering. In the second model, we consider the facility's moving cost between adjacent stages under the social cost objective. The social cost additionally includes the total travel distance of the facility. Correspondingly, we design XP (and polynomial time) algorithms and a group strategy-proof meanism for settings with or without the FCFS ordering.