Fair Transit Stop Placement: A Clustering Perspective and Beyond

TL;DR

This paper explores fair transit stop placement in metric spaces, establishing theoretical bounds for fairness notions and proposing algorithms with tunable fairness trade-offs, supported by experimental validation.

Contribution

It introduces a structural link between fair clustering and transit stop placement, proposes algorithms with approximation guarantees, and analyzes fairness bounds.

Findings

Constant-factor approximation for proportional fairness in clustering.

Lower bound of 1.366 on approximability of justified representation.

Proposed Expanding Cost Algorithm achieves a 2.414-approximation for JR.

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.