Fair Transit Stop Placement: A Clustering Perspective and Beyond
This work addresses fairness in transit planning for urban mobility, offering incremental algorithmic improvements with theoretical guarantees.
The paper tackles the transit stop placement problem by incorporating fairness concepts like justified representation and the core, showing a connection to fair clustering and providing approximation algorithms with theoretical bounds, including a 2.414-approximation for JR and a tunable trade-off between JR and core.
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.