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We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.
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This content will become publicly available on June 5, 2026
Group Fairness in Multi-period Mobile Facility Location Problems
We study the group-fair multi-period mobile facility location problems, where agents from different groups are located on a real line and arrive in different periods. Our goal is to locate k mobile facilities at each period to serve the arriving agents in order to minimize the maximum total group-fair cost and the maximum average group-fair cost objectives that measure the costs or distances of groups of agents to their corresponding facilities across all periods. We first consider the problems from the algorithmic perspective for both group-fair cost objectives. We then consider the problems from the mechanism design perspective, where the agents' locations and arrival periods are private. For both objectives, we design deterministic strategyproof mechanisms to elicit the agents' locations and arrival periods truthfully while optimizing the group-fair cost objectives and show that our mechanisms have almost tight bounds on the approximation ratios for certain periods and settings. Finally, we discuss the extensions of our results to the online setting where agent arrival information is only known at each period.
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- PAR ID:
- 10611349
- Publisher / Repository:
- International Foundation for Autonomous Agents and Multiagent Systems
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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