Adapting Dijkstra for Buffers and Unlimited Transfers

TL;DR

This paper revisits classical Dijkstra-based algorithms for public transit routing, introducing Transfer Aware Dijkstra (TAD) to handle buffer times effectively and outperform existing methods.

Contribution

The paper introduces TAD, a modified Dijkstra algorithm that correctly accounts for buffer times in transit routing, improving performance over MR.

Findings

TAD achieves over two times speed-up compared to MR.

TAD produces optimal routing results with and without buffer times.

Filtering dominated connections is unsound with buffer times, motivating TAD.

Abstract

In recent years, RAPTOR based algorithms have been considered the state-of-the-art for path-finding with unlimited transfers without preprocessing. However, this status largely stems from the evolution of routing research, where Dijkstra-based solutions were superseded by timetable-based algorithms without a systematic comparison. In this work, we revisit classical Dijkstra-based approaches for public transit routing with unlimited transfers and demonstrate that Time-Dependent Dijkstra (TD-Dijkstra) outperforms MR. However, efficient TD-Dijkstra implementations rely on filtering dominated connections during preprocessing, which assumes passengers can always switch to a faster connection. We show that this filtering is unsound when stops have buffer times, as it cannot distinguish between seated passengers who may continue without waiting and transferring passengers who must respect the buffer. To address this limitation, we introduce Transfer Aware Dijkstra (TAD), a modification that scans entire trip sequences rather than individual edges, correctly handling buffer times while maintaining performance advantages over MR. Our experiments on London and Switzerland networks show that we can achieve a greater than two time speed-up over MR while producing optimal results on both networks with and without buffer times.