Document Open Access Logo

T-REX: Fast and Dynamic Journey Planning for Continental-Scale Public Transit Networks

Authors Jonas Sauer , Patrick Steil , Sascha Witt

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2026.9.pdf
  • Filesize: 0.99 MB
  • 25 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
  • Mathematics of computing → Graph algorithms
  • Applied computing → Transportation
Keywords
  • Public transit routing
  • graph algorithms
  • algorithm engineering

Metrics

Abstract

We present T-REX (Transfer-Ranked EXploration), a new algorithm for journey planning in public transit networks on the country and continental scale. Our algorithm applies the principles of multi-level overlays to Trip-Based Public Transit Routing (TB). Using a multi-level partition of the network, T-REX identifies transfers between trips that are relevant for long-distance travel in a short precomputation phase. This information is then used to prune irrelevant local transfers during a query. Like other state-of-the-art algorithms, T-REX Pareto-optimizes arrival time and the number of used trips. T-REX dramatically outperforms previous overlay-based algorithms for three key reasons: (1) a better partition, (2) reducing the search space by focusing on transfers rather than trips, and (3) a redesigned query algorithm with improved memory efficiency and throughput. As a result, T-REX answers queries in less than 10ms on a network of Europe, including local and long-distance transit. This constitutes a speedup of 20 compared to TB and 80 compared to algorithms without preprocessing. The memory footprint is moderate and the precomputation takes only two minutes, while real-time schedule updates can be incorporated in a few seconds. These properties make T-REX the first public transit journey planning algorithm that fulfills the requirements of interactive real-time applications on the continental scale.

Cite As Get BibTex

Jonas Sauer, Patrick Steil, and Sascha Witt. T-REX: Fast and Dynamic Journey Planning for Continental-Scale Public Transit Networks. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 9:1-9:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.9

Author Details

Jonas Sauer
  • Karlsruhe Institute of Technology, Germany
Patrick Steil
  • Karlsruhe Institute of Technology, Germany
Sascha Witt
  • Karlsruhe Institute of Technology, Germany

Acknowledgements

We thank Christian Schulz for providing us with the original implementation of KaHIP, Lars Gottesbüren and Nikolai Maas for advice on configuring Mt-KaHyPar, Ben Strasser for providing us with the original implementations of CSA and ACSA, and Patrick Brosi and Transitous (https://transitous.org/) for supplying the Germany and Europe datasets used in our experiments.

Supplementary Materials

References

  1. Prateek Agarwal and Tarun Rambha. Scalable algorithms for bicriterion trip-based transit routing, 2021. URL: https://arxiv.org/abs/2111.06654.
  2. Hannah Bast. Car or public transport - two worlds. In Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday, volume 5760 of Lecture Notes in Computer Science (LNCS), pages 355-367. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-03456-5_24.
  3. Hannah Bast, Erik Carlsson, Arno Eigenwillig, Robert Geisberger, Chris Harrelson, Veselin Raychev, and Fabien Viger. Fast routing in very large public transportation networks using transfer patterns. In Proceedings of the 18th Annual European Symposium on Algorithms (ESA'10), volume 6346 of Lecture Notes in Computer Science (LNCS), pages 290-301. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15775-2_25.
  4. Hannah Bast, Daniel Delling, Andrew V. Goldberg, Matthias Müller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato F. Werneck. Route planning in transportation networks. In Algorithm Engineering: Selected Results and Surveys, volume 9220 of Lecture Notes in Computer Science (LNCS), pages 19-80. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-49487-6_2.
  5. Hannah Bast, Matthias Hertel, and Sabine Storandt. Scalable transfer patterns. In Proceedings of the 18th Workshop on Algorithm Engineering and Experiments (ALENEX'16), pages 15-29. Society for Industrial and Applied Mathematics, 2016. URL: https://doi.org/10.1137/1.9781611974317.2.
  6. Hannah Bast, Jonas Sternisko, and Sabine Storandt. Delay-robustness of transfer patterns in public transportation route planning. In Proceedings of the 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'13), volume 33 of OpenAccess Series in Informatics (OASIcs), pages 42-54. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2013. URL: https://doi.org/10.4230/OASIcs.ATMOS.2013.42.
  7. Reinhard Bauer, Daniel Delling, and Dorothea Wagner. Experimental study on speed-up techniques for timetable information systems. In Proceedings of the 7th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'07), volume 7 of OpenAccess Series in Informatics (OASIcs). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2007. URL: https://doi.org/10.4230/OASIcs.ATMOS.2007.1169.
  8. Moritz Baum, Valentin Buchhold, Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. ULTRA: Unlimited transfers for efficient multimodal journey planning. Transportation Science, 57:1536-1559, 2023. URL: https://doi.org/10.1287/trsc.2022.0198.
  9. Annabell Berger, Daniel Delling, Andreas Gebhardt, and Matthias Müller-Hannemann. Accelerating time-dependent multi-criteria timetable information is harder than expected. In Proceedings of the 9th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'09), volume 12 of OpenAccess Series in Informatics (OASIcs), pages 2:1-2:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009. URL: https://doi.org/10.4230/OASIcs.ATMOS.2009.2148.
  10. Thomas Bläsius, Valentin Buchhold, Dorothea Wagner, Tim Zeitz, and Michael Zündorf. Customizable contraction hierarchies - A survey, 2025. URL: https://doi.org/10.48550/arXiv.2502.10519.
  11. Gerth S. Brodal and Riko Jacob. Time-dependent networks as models to achieve fast exact time-table queries. In Proceedings of the 3rd Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'03), volume 92, pages 3-15. Elsevier, 2004. URL: https://doi.org/10.1016/j.entcs.2003.12.019.
  12. Alessio Cionini, Gianlorenzo D'Angelo, Mattia D'Emidio, Daniele Frigioni, Kalliopi Giannakopoulou, Andreas Paraskevopoulos, and Christos Zaroliagis. Engineering graph-based models for dynamic timetable information systems. Journal of Discrete Algorithms, 46-47:40-58, 2017. URL: https://doi.org/10.1016/j.jda.2017.09.001.
  13. Edith Cohen, Eran Halperin, Haim Kaplan, and Uri Zwick. Reachability and distance queries via 2-hop labels. SIAM Journal on Computing, 32(5):1338-1355, 2003. URL: https://doi.org/10.1137/S0097539702403098.
  14. Daniel Delling, Julian Dibbelt, Thomas Pajor, and Renato F. Werneck. Public transit labeling. In Proceedings of the 14th International Symposium on Experimental Algorithms (SEA'15), volume 9125 of Lecture Notes in Computer Science (LNCS), pages 273-285. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-20086-6_21.
  15. Daniel Delling, Julian Dibbelt, Thomas Pajor, and Tobias Zündorf. Faster transit routing by hyper partitioning. In Proceedings of the 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'17), volume 59 of OpenAccess Series in Informatics (OASIcs), pages 8:1-8:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/OASIcs.ATMOS.2017.8.
  16. Daniel Delling, Andrew V. Goldberg, Thomas Pajor, and Renato F. Werneck. Customizable route planning in road networks. Transportation Science, 51(2):566-591, 2017. URL: https://doi.org/10.1287/TRSC.2014.0579.
  17. Daniel Delling, Thomas Pajor, and Dorothea Wagner. Engineering time-expanded graphs for faster timetable information. In Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems, volume 5868 of Lecture Notes in Computer Science (LNCS), pages 182-206. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-05465-5_7.
  18. Daniel Delling, Thomas Pajor, and Renato F. Werneck. Round-based public transit routing. Transportation Science, 49(3):591-604, 2015. URL: https://doi.org/10.1287/TRSC.2014.0534.
  19. Mattia D'Emidio, Imran Khan, and Daniele Frigioni. Journey planning algorithms for massive delay-prone transit networks. Algorithms, 13(1):2, 2020. URL: https://doi.org/10.3390/A13010002.
  20. Julian Dibbelt, Thomas Pajor, Ben Strasser, and Dorothea Wagner. Connection scan algorithm. Journal of Experimental Algorithmics, 23, 2018. URL: https://doi.org/10.1145/3274661.
  21. Julian Dibbelt, Ben Strasser, and Dorothea Wagner. Customizable contraction hierarchies. Journal of Experimental Algorithmics, 21:1.5:1-1.5:49, 2016. URL: https://doi.org/10.1145/2886843.
  22. Edsger W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269-271, 1959. URL: https://doi.org/10.1007/BF01386390.
  23. Yann Disser, Matthias Müller-Hannemann, and Mathias Schnee. Multi-criteria shortest paths in time-dependent train networks. In Proceedings of the 7th International Workshop on Experimental and Efficient Algorithms (WEA'08), volume 5038 of Lecture Notes in Computer Science (LNCS), pages 347-361. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-68552-4_26.
  24. Alexandros Efentakis and Dieter Pfoser. GRASP. Extending graph separators for the single-source shortest-path problem. In Proceedings of the 22nd Annual European Symposium on Algorithms (ESA'14), volume 8737 of Lecture Notes in Computer Science (LNCS), pages 358-370. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-44777-2_30.
  25. Robert Geisberger, Peter Sanders, Dominik Schultes, and Christian Vetter. Exact routing in large road networks using contraction hierarchies. Transportation Science, 46(3):388-404, 2012. URL: https://doi.org/10.1287/trsc.1110.0401.
  26. Kalliopi Giannakopoulou, Andreas Paraskevopoulos, and Christos Zaroliagis. Multimodal dynamic journey-planning. Algorithms, 12(10), 2019. URL: https://doi.org/10.3390/a12100213.
  27. GitHub repository: TransitRouting/FLASH-TB. https://github.com/TransitRouting/FLASH-TB. [Accessed 04-03-2026].
  28. GitHub repository: patrickbr/gtfstidy. https://github.com/patrickbr/gtfstidy. [Accessed 04-03-2026].
  29. GitHub repository: KaHIP/KaHIP. https://github.com/KaHIP/KaHIP. [Accessed 04-03-2026].
  30. GitHub repository: kahypar/mt-kahypar. https://github.com/kahypar/mt-kahypar. [Accessed 04-03-2026].
  31. GitHub repository: PatrickSteil/mt-kahypar. https://github.com/PatrickSteil/mt-kahypar. [Accessed 04-03-2026].
  32. Andrew V. Goldberg and Chris Harrelson. Computing the shortest path: A* search meets graph theory. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05), pages 156-165. Society for Industrial and Applied Mathematics, 2005. URL: https://doi.org/10.5555/1070432.1070455.
  33. Lars Gottesbüren. Parallel and Flow-Based High-Quality Hypergraph Partitioning. PhD thesis, Karlsruhe Institute of Technology, 2023. URL: https://doi.org/10.5445/IR/1000157894.
  34. Lars Gottesbüren and Michael Hamann. Deterministic parallel hypergraph partitioning. In Proceedings of the 28th International Conference on Parallel and Distributed Computing (Euro-Par'22), volume 13440, pages 301-316. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-12597-3_19.
  35. Lars Gottesbüren, Michael Hamann, Tim Niklas Uhl, and Dorothea Wagner. Faster and better nested dissection orders for customizable contraction hierarchies. Algorithms, 12(9):196, 2019. URL: https://doi.org/10.3390/A12090196.
  36. Lars Gottesbüren, Tobias Heuer, Nikolai Maas, Peter Sanders, and Sebastian Schlag. Scalable high-quality hypergraph partitioning. ACM Transactions on Algorithms, 20(1):9:1-9:54, 2024. URL: https://doi.org/10.1145/3626527.
  37. Ernestine Großmann, Jonas Sauer, Christian Schulz, Patrick Steil, and Sascha Witt. FLASH-TB: Integrating arc-flags and trip-based public transit routing. Transportation Science, 60(2):242-263, 2026. URL: https://doi.org/10.1287/trsc.2023.0481.
  38. GTFS für Deutschland. https://gtfs.de/. [Accessed 04-03-2026].
  39. General Transit Feed Specification. https://gtfs.org/. [Accessed 04-03-2026].
  40. Michael Hamann and Ben Strasser. Graph bisection with Pareto optimization. Journal of Experimental Algorithmics, 23:1.2:1-1.2:34, 2018. URL: https://doi.org/10.1145/3173045.
  41. Peter E. Hart, Nils J. Nilsson, , and Bertram Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4:100-107, 1968. URL: https://doi.org/10.1109/TSSC.1968.300136.
  42. Moritz Hilger, Ekkehard Köhler, Rolf H. Möhring, and Heiko Schilling. Fast point-to-point shortest path computations with arc-flags. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, volume 74 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 41-72. American Mathematical Society, 2009. URL: https://doi.org/10.1090/dimacs/074/03.
  43. Martin Holzer, Frank Schulz, and Dorothea Wagner. Engineering multilevel overlay graphs for shortest-path queries. Journal of Experimental Algorithmics, 13(2.5):1-26, 2008. URL: https://doi.org/10.5555/2791171.2791186.
  44. Sungwon Jung and Sakti Pramanik. An efficient path computation model for hierarchically structured topographical road maps. IEEE Transactions on Knowledge and Data Engineering, 14:1029-1046, 2002. URL: https://doi.org/10.1109/TKDE.2002.1033772.
  45. Ulrich Lauther. An experimental evaluation of point-to-point shortest path calculation on road networks with precalculated edge-flags. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, volume 74 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 19-40. American Mathematical Society, 2009. URL: https://doi.org/10.1090/dimacs/074/02.
  46. Vassilissa Lehoux and Christelle Loiodice. Faster preprocessing for the trip-based public transit routing algorithm. In Proceedings of the 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'20), volume 85 of OpenAccess Series in Informatics (OASIcs), pages 3:1-3:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/OASIcs.ATMOS.2020.3.
  47. Rolf H. Möhring, Heiko Schilling, Birk Schütz, Dorothea Wagner, and Thomas Willhalm. Partitioning graphs to speedup Dijkstra’s algorithm. Journal of Experimental Algorithmics, 11(2.8):1-29, 2006. URL: https://doi.org/10.1145/1187436.1216585.
  48. Matthias Müller-Hannemann and Mathias Schnee. Finding all attractive train connections by multi-criteria Pareto search. In Algorithmic Methods for Railway Optimization, volume 4359 of Lecture Notes in Computer Science (LNCS), pages 246-263. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74247-0_13.
  49. Matthias Müller-Hannemann and Mathias Schnee. Efficient timetable information in the presence of delays. In Robust and Online Large-Scale Optimization, volume 5868 of Lecture Notes in Computer Science (LNCS), pages 249-272. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-05465-5_10.
  50. Evangelia Pyrga, Frank Schulz, Dorothea Wagner, and Christos D. Zaroliagis. Efficient models for timetable information in public transportation systems. Journal of Experimental Algorithmics, 12:2.4:1-2.4:39, 2008. URL: https://doi.org/10.1145/1227161.1227166.
  51. Peter Sanders and Christian Schulz. Think locally, act globally: Highly balanced graph partitioning. In Proceedings of the 12th International Symposium on Experimental Algorithms (SEA'13), volume 7933 of Lecture Notes in Computer Science (LNCS), pages 164-175. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38527-8_16.
  52. Jonas Sauer, Patrick Steil, and Sascha Witt. PatrickSteil/TREX. Software, (visited on 2026-08-11). URL: https://github.com/PatrickSteil/TREX
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.27611
  53. Jonas Sauer, Patrick Steil, and Sascha Witt. Datasets for "T-REX: Fast and dynamic journey planning for continental-scale public transit networks", April 2026. URL: https://doi.org/10.5281/zenodo.19697732.
  54. Jonas Sebastian Sauer. Closing the Performance Gap Between Multimodal and Public Transit Journey Planning. PhD thesis, Karlsruher Institut für Technologie (KIT), 2024. URL: https://doi.org/10.5445/IR/1000173225.
  55. Aaron Schild and Christian Sommer. On balanced separators in road networks. In Proceedings of the 14th International Symposium on Experimental Algorithms (SEA'15), volume 9125 of Lecture Notes in Computer Science (LNCS), pages 286-297. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-20086-6_22.
  56. Sebastian Schlag, Vitali Henne, Tobias Heuer, Henning Meyerhenke, Peter Sanders, and Christian Schulz. k-way hypergraph partitioning via n-level recursive bisection. In Proceedings of the 18th Workshop on Algorithm Engineering and Experiments (ALENEX'16), pages 53-67. Society for Industrial and Applied Mathematics, 2016. URL: https://doi.org/10.1137/1.9781611974317.5.
  57. Frank Schulz, Dorothea Wagner, and Christos D. Zaroliagis. Using multi-level graphs for timetable information in railway systems. In Proceedings of the 4th Workshop on Algorithm Engineering and Experiments (ALENEX'02), volume 2409 of Lecture Notes in Computer Science (LNCS), pages 43-59. Springer, 2002. URL: https://doi.org/10.5555/646680.702320.
  58. Patrick Steil. A multilevel design for scalable Pareto-optimal public transit queries. Master’s thesis, Karlsruher Institut für Technologie (KIT), 2025. URL: https://doi.org/10.5445/IR/1000190843.
  59. Transitous. https://transitous.org/. [Accessed 04-03-2026].
  60. Sascha Witt. Trip-based public transit routing. In Proceedings of the 23rd Annual European Symposium on Algorithms (ESA'15), volume 9294 of Lecture Notes in Computer Science (LNCS), pages 1025-1036. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-48350-3_85.
  61. Sascha Witt. Trip-based public transit routing using condensed search trees. In Proceedings of the 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'16), volume 54 of OpenAccess Series in Informatics (OASIcs), pages 10:1-10:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/OASIcs.ATMOS.2016.10.
  62. Sascha Witt. Extending the time horizon: Efficient public transit routing on arbitrary-length timetables, 2021. URL: https://arxiv.org/abs/2109.14143.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact