Fair Transit Stop Placement: A Clustering Perspective and Beyond

2026-02-06

AI Summary

This study addresses the fairness of bus stop placement in general metric spaces, aiming to achieve proportionally fair coverage between walking access and feeder service. By establishing a theoretical connection to fair clustering, the work reveals structural links to Justified Representation (JR) and core stability. The authors propose a tunable parameterized algorithm that enables a controllable trade-off between JR and core fairness, and prove a lower bound of 1.366 on the approximation ratio for JR. Furthermore, they design a tight 2.414-approximation algorithm for JR by integrating an Expanding Cost framework with a parameterized interpolation strategy, supported by a two-parameter approximation analysis. Experiments on real-world ride-pooling data demonstrate the effectiveness and practicality of the proposed approach.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the transit stop placement (TrSP) problem in general metric spaces, where agents travel between source-destination pairs and may either walk directly or utilize a shuttle service via selected transit stops. We investigate fairness in TrSP through the lens of justified representation (JR) and the core, and uncover a structural correspondence with fair clustering. Specifically, we show that a constant-factor approximation to proportional fairness in clustering can be used to guarantee a constant-factor biparameterized approximation to core. We establish a lower bound of 1.366 on the approximability of JR, and moreover show that no clustering algorithm can approximate JR within a factor better than 3. Going beyond clustering, we propose the Expanding Cost Algorithm, which achieves a tight 2.414-approximation for JR, but does not give any bounded core guarantee. In light of this, we introduce a parameterized algorithm that interpolates between these approaches, and enables a tunable trade-off between JR and core. Finally, we complement our results with an experimental analysis using small-market public carpooling data.

Problem

• Transit Stop Placement
• Fairness
• Justified Representation
• Core
• Metric Spaces

Innovation

• Fair Transit Stop Placement
• Justified Representation
• Core
• Fair Clustering
• Approximation Algorithm