Adapting Dijkstra for Buffers and Unlimited Transfers

2026-03-12

AI Summary

This work addresses a critical limitation in existing Dijkstra-based public transit routing methods, which erroneously prune connections during domination checks due to neglecting passenger state distinctions—such as whether a traveler is transferring or already seated—when handling station buffer times and unlimited transfers. To resolve this, the authors propose Transfer-Aware Dijkstra (TAD), the first algorithm within a time-dependent Dijkstra framework that accurately models the impact of buffer times on different passenger states by scanning entire trip sequences rather than individual edges, thereby avoiding incorrect pruning inherent in conventional preprocessing. Experimental results on the London and Swiss transit networks demonstrate that TAD achieves more than a two-fold speedup over the MR algorithm while consistently returning optimal paths, regardless of whether buffer times are considered.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Application Domains: Transportation
• Search and Optimization: Algorithm Configuration

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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 However, this status largely stems from the evolution of routing research, where Dijkstra-based solutions were superseded by timetable-based algorithms without a systematic comparison.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.

Problem

• public transit routing
• unlimited transfers
• buffer times
• Time-Dependent Dijkstra
• connection filtering

Innovation

• Transfer Aware Dijkstra
• Time-Dependent Dijkstra
• buffer times
• unlimited transfers
• public transit routing