Early Pruning for Public Transport Routing

Abstract: 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.

• The paper introduces Early Pruning, a provably optimality-preserving method that sorts outgoing transfer edges by duration and stops relaxation when later edges cannot improve the target result.
• Experiments on Switzerland and London networks show speedups of up to 56.9% for McRAPTOR, with the largest gains on dense transitive transfer graphs and smaller benefits for ULTRA-based variants.
• The timetable-independent preprocessing costs under 600 milliseconds per network, enabling richer walking and multimodal connections while avoiding schedule-dependent shortcut recomputation.

Motivation and problem statement

RAPTOR and its variants dominate production transit routing, powering systems such as Bing Maps, OpenTripPlanner, R5, and Navitia. Their principal bottleneck is the transfer relaxation phase, in which the algorithm iterates over outgoing transfer edges from every stop updated in the previous round. When the transfer graph is dense—whether because it is transitively closed, or because it incorporates walking, cycling, and micro-mobility connections—this phase dominates total query time. In practice, agencies respond by capping transfer distances or dropping modes, which sacrifices path optimality and narrows the multimodal options presented to travellers. This paper, accepted at WCTR 2026, introduces Early Pruning, a low-overhead technique that removes a large fraction of this work without compromising optimality (2603.12592).

The technique

Early Pruning exploits a simple monotonicity property. All outgoing transfer edges at each stop are pre-sorted in non-decreasing order of duration, a one-time preprocessing step. During transfer relaxation, if the arrival time at the head of an edge $e_i = (s, v_i)$ already satisfies $\tau_k(s) + \tau(e_i) \geq \tau^*(t)$, where $\tau^*(t)$ is the best known arrival at the target, then every subsequent edge $e_j$, $j > i$, yields an arrival at least as late, and the entire iteration can be terminated. Because the sort order guarantees this, no candidate is discarded incorrectly, so the method preserves optimality exactly.

The rule generalises to multi-criteria settings (McRAPTOR, ULTRA-McRAPTOR, BM-RAPTOR, UBM-RAPTOR) by replacing scalar comparison with Pareto dominance: since walking duration increases monotonically along the sorted edge sequence, once a partial path is dominated at the target in all criteria (arrival time, walking duration, number of transfers), no later edge can produce a non-dominated result. The authors prove correctness for both the single-criterion and extended-criterion settings.

The idea is closely related to target pruning in the original RAPTOR and to the sorted hub lists used by Phan and Viennot for hub labelling, but Early Pruning applies the principle directly inside the transfer relaxation loop without hub label preprocessing, and extends it to additional criteria.

Experimental evaluation

The evaluation covers six RAPTOR variants on the Switzerland (25,125 stops, 3.2M transitive edges) and London (19,682 stops, 2.6M transitive edges) networks, using the KIT reference implementation with 1,000 random queries per configuration. Edge sorting requires under 600 ms per network and, crucially, is independent of timetable data—it need not be recomputed when schedules change, unlike ULTRA shortcuts.

Algorithm	Network	Baseline	Early Pruning	Speedup
RAPTOR	Switzerland (transitive)	53.8 ms	42.1 ms	21.7%
RAPTOR	London (transitive)	48.6 ms	32.2 ms	33.9%
McRAPTOR	Switzerland (transitive)	2997 ms	1646 ms	45.1%
McRAPTOR	London (transitive)	3966 ms	1707 ms	56.9%
ULTRA-RAPTOR	Switzerland (shortcuts)	44.3 ms	39.4 ms	11.1%
ULTRA-McRAPTOR	Switzerland (Mc shortcuts)	749 ms	731 ms	2.4%
BM-RAPTOR	London (transitive)	258 ms	217 ms	16.0%
UBM-RAPTOR	London (Mc shortcuts)	82 ms	77 ms	6.1%

The headline result is a 56.9% query time reduction for McRAPTOR on London, cutting a ~4-second multi-criteria query to under 2 seconds—within interactive-response range. Gains are largest for algorithms operating on dense transitive graphs (RAPTOR, McRAPTOR, BM-RAPTOR) and smallest on ULTRA shortcut graphs, which contain roughly two orders of magnitude fewer edges. The paper reports a Pearson correlation of 0.62 ($p \approx 0.033$) between graph density and speedup, supporting the claim that denser transfer graphs benefit more. A notable negative result: applying the same idea to CSA yields no practical improvement, which the authors attribute to CSA's smaller memory footprint and cache behaviour during connection scanning.

Policy and planning implications

The authors argue that the speedups relax the trade-off between multimodal richness and response time. For example, the 34% RAPTOR speedup on London could allow an agency to raise the transitive-closure threshold from 4 minutes to a longer duration at constant query time, admitting more walking connections. Because Early Pruning's preprocessing is timetable-independent, it is inherently robust to real-time disruptions and suits dynamic environments where ULTRA shortcuts would require recomputation. The equity argument is that under tight computational budgets, complex multimodal transfers are dropped first—precisely the options that matter in outer suburbs with sparse direct coverage—so cheaper routing can surface car-alternative journeys there.

Limitations and open questions

Several caveats are stated plainly. The benefit on ULTRA-based variants is modest (1.6–13.6%), so the technique's value depends on the algorithm and graph representation in use. The density–speedup correlation rests on only twelve algorithm–network configurations and one network pair, and the authors themselves concede uncertainty about the cause of London's slower edge sorting despite fewer edges. The claim that Early Pruning suits dynamic scenarios is asserted without dedicated experiments. The evaluation uses the KIT reference implementation, which is not the codebase deployed in widely used open-source planners; integration into OpenTripPlanner or R5 remains untested. The CSA result also indicates the technique is not universally transferable across transit routing architectures.

Conclusion

Early Pruning is a minimal, provably optimality-preserving modification to RAPTOR-family transfer relaxation that delivers consistent, sometimes large speedups—up to 57% on multi-criteria queries—at the cost of a sub-second, timetable-independent preprocessing step. Its effectiveness scales with transfer graph density, making it most valuable exactly where multimodal integration makes routing hardest. The main open question is how the technique performs in production-grade open-source planners and in genuinely dynamic settings, neither of which is evaluated here.