Timetable Nodes for Public Transport Network

TL;DR

This paper introduces timetable nodes (TTN), a novel pre-computation method using computational geometry to significantly speed up pathfinding in public transport networks, outperforming traditional graph-based approaches.

Contribution

It proposes a new TTN pre-computation technique with two implementations that reduce complexity and improve search speed in time-dependent transport networks.

Findings

TTN methods reduce asymptotic complexity from O(k log|C|) to O(k + log(k) + log|C|)

Experimental results show significant performance improvements on high-density graphs

The approach can be integrated into existing pathfinding algorithms for various time-dependent networks

Abstract

Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The solutions that work well in road networks, such as Time-dependent Contraction Hierarchies and other graph-based approaches, do not usually apply in transport networks. In transport networks, non-graph solutions such as CSA and RAPTOR show the best results compared to graph-based techniques. In our work, we propose a method that advances graph-based approaches by using different optimization techniques from computational geometry to speed up the search process in transport networks. We apply a new pre-computation step, which we call timetable nodes (TTN). Our inspiration comes from an iterative search problem in computational geometry. We implement two versions of the TTN: one uses a Combined Search Tree (TTN-CST), and the second uses Fractional Cascading (TTN-FC). Both of these approaches decrease the asymptotic complexity of reaching new nodes from $O(k\times \log|C|)$ to $O(k + \log(k) + \log(|C|))$, where $k$ is the number of outgoing edges from a node and $|C|$ is the size of the timetable information (total outgoing edges). Our solution suits any other time-dependent networks and can be integrated into other pathfinding algorithms. Our experiments indicate that this pre-computation significantly enhances the performance on high-density graphs. This study showcases how leveraging computational geometry can enhance pathfinding in transport networks, enabling faster pathfinding in scenarios involving large numbers of outgoing edges.