Early Pruning for Public Transport Routing

Routing algorithms for public transport, particularly the widely used RAPTOR and its variants, often face performance bottlenecks during the transfer relaxation phase, especially on dense transfer graphs, when supporting unlimited transfers. This inefficiency arises from iterating over many potential inter-stop connections (walks, bikes, e-scooters, etc.). To maintain acceptable performance, practitioners often limit transfer distances or exclude certain transfer options, which can reduce path optimality and restrict the multimodal options presented to travellers. This paper introduces Early Pruning, a low-overhead technique that accelerates routing algorithms without compromising optimality. By pre-sorting transfer connections by duration and applying a pruning rule within the transfer loop, the method discards longer transfers at a stop once they cannot yield an earlier arrival than the current best solution. Early Pruning can be integrated with minimal changes to existing codebases and requires only a one-time preprocessing step. Across multiple state-of-the-art RAPTOR-based solutions, including RAPTOR, ULTRA-RAPTOR, McRAPTOR, BM-RAPTOR, ULTRA-McRAPTOR, and UBM-RAPTOR and tested on the Switzerland and London transit networks, we achieved query time reductions of up to 57%. This approach provides a generalizable improvement to the efficiency of transit pathfinding algorithms. Beyond algorithmic performance, Early Pruning has practical implications for transport planning. By reducing computational costs, it enables transit agencies to expand transfer radii and incorporate additional mobility modes into journey planners without requiring extra server infrastructure. This is particularly relevant for passengers in areas with sparse direct transit coverage, such as outer suburbs and smaller towns, where richer multimodal routing can reveal viable alternatives to private car use.

Adapting Dijkstra for Buffers and Unlimited Transfers

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 However, this status largely stems from the evolution of routing research, where Dijkstra-based solutions were superseded by timetable-based algorithms without a systematic comparison.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

Timetable Nodes for Public Transport Network

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.