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Continuous Map Matching to Paths Under Travel Time Constraints

Authors Yannick Bosch , Sabine Storandt

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LIPIcs.SEA.2025.7.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Computational geometry
Keywords
  • Map matching
  • Travel time
  • Segment-circle intersection data structure

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Abstract

In this paper, we study the problem of map matching with travel time constraints. Given a sequence of k spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by location in the graph, such that consecutive locations can be reached from one another along the path within the timestamp difference of the respective measurements. This problem arises in public transit data processing as well as in map matching of movement trajectories to general graphs. We show that the classical approach for this problem, which relies on selecting a finite set of candidate locations in the graph for each measurement, cannot guarantee to find a consistent solution. We propose a new algorithm that can deal with an infinite set of candidate locations per measurement. We prove that our algorithm always detects a consistent map matching path (if one exists). Despite the enlarged candidate set, we also demonstrate that our algorithm has superior running time in theory and practice. For a path graph with n nodes, we show that our algorithm runs in 𝒪(k² n log {nk}) and under mild assumptions in 𝒪(k n ^λ + n log³ n) for λ ≈ 0.695. This is a significant improvement over the baseline, which runs in 𝒪(k n²) and which might not even identify a correct solution. The performance of our algorithm hinges on an efficient segment-circle intersection data structure. We describe how to design and implement such a data structure for our application. In the experimental evaluation, we demonstrate the usefulness of our novel algorithm on a diverse set of generated measurements as well as GTFS data.

Cite As Get BibTex

Yannick Bosch and Sabine Storandt. Continuous Map Matching to Paths Under Travel Time Constraints. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.7

Author Details

Yannick Bosch
  • University of Konstanz, Germany
Sabine Storandt
  • University of Konstanz, Germany

References

  1. Hannah Bast and Patrick Brosi. Sparse map-matching in public transit networks with turn restrictions. In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 480-483, 2018. URL: https://doi.org/10.1145/3274895.3274957.
  2. David Bernstein, Alain Kornhauser, et al. An introduction to map matching for personal navigation assistants, 1996. New Jersey TIDE Center. Google Scholar
  3. Sotiris Brakatsoulas, Dieter Pfoser, Randall Salas, and Carola Wenk. On map-matching vehicle tracking data. In Proceedings of the 31st international conference on Very large data bases, pages 853-864, 2005. URL: http://www.vldb.org/archives/website/2005/program/paper/fri/p853-brakatsoulas.pdf.
  4. Erin Chambers, Brittany Terese Fasy, Yusu Wang, and Carola Wenk. Map-matching using shortest paths. ACM Transactions on Spatial Algorithms and Systems (TSAS), 6(1):1-17, 2020. URL: https://doi.org/10.1145/3368617.
  5. Bernard Chazelle and Emo Welzl. Quasi-optimal range searching in spaces of finite vc-dimension. Discrete & Computational Geometry, 4:467-489, 1989. URL: https://doi.org/10.1007/BF02187743.
  6. Daniel Chen, Anne Driemel, Leonidas J Guibas, Andy Nguyen, and Carola Wenk. Approximate map matching with respect to the fréchet distance. In 2011 Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments (ALENEX), pages 75-83. SIAM, 2011. URL: https://doi.org/10.1137/1.9781611972917.8.
  7. Siu Wing Cheng and Ravi Janardan. Algorithms for ray-shooting and intersection searching. Journal of Algorithms, 13(4):670-692, 1992. URL: https://doi.org/10.1016/0196-6774(92)90062-H.
  8. Wonhee Cho and Eunmi Choi. A basis of spatial big data analysis with map-matching system. Cluster Computing, 20(3):2177-2192, 2017. URL: https://doi.org/10.1007/S10586-017-1014-1.
  9. Bram Custers, Wouter Meulemans, Marcel Roeloffzen, Bettina Speckmann, and Kevin Verbeek. Physically consistent map matching. In Proceedings of the 30th International Conference on Advances in Geographic Information Systems, pages 1-4, 2022. URL: https://doi.org/10.1145/3557915.3560991.
  10. Hendrik Edelhoff, Johannes Signer, and Niko Balkenhol. Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns. Movement ecology, 4:1-21, 2016. Google Scholar
  11. Jochen Eisner, Stefan Funke, Andre Herbst, Andreas Spillner, and Sabine Storandt. Algorithms for matching and predicting trajectories. In 2011 Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments (ALENEX), pages 84-95. SIAM, 2011. URL: https://doi.org/10.1137/1.9781611972917.9.
  12. Stefan Funke, Tobias Rupp, André Nusser, and Sabine Storandt. Pathfinder: storage and indexing of massive trajectory sets. In Proceedings of the 16th International Symposium on Spatial and Temporal Databases, pages 90-99, 2019. URL: https://doi.org/10.1145/3340964.3340978.
  13. geOps. Snapping stops: Matching stops to the network, n.d. Accessed: 2025-01-03. URL: https://geops.com/de/blog/snapping-stops.
  14. Luca Giovannini. A novel map-matching procedure for low-sampling gps data with applications to traffic flow analysis, 2011. University of Bologna. Google Scholar
  15. Chong Yang Goh, Justin Dauwels, Nikola Mitrovic, Muhammad Tayyab Asif, Ali Oran, and Patrick Jaillet. Online map-matching based on hidden markov model for real-time traffic sensing applications. In 2012 15th International IEEE Conference on Intelligent Transportation Systems, pages 776-781. IEEE, 2012. URL: https://doi.org/10.1109/ITSC.2012.6338627.
  16. Joachim Gudmundsson, Martin P Seybold, and Sampson Wong. Map matching queries on realistic input graphs under the fréchet distance. ACM Transactions on Algorithms, 20(2):1-33, 2024. Google Scholar
  17. Prosenjit Gupta, Ravi Janardan, and Michiel Smid. On intersection searching problems involving curved objects. In Algorithm Theory—SWAT'94: 4th Scandinavian Workshop on Algorithm Theory Aarhus, Denmark, July 6-8, 1994 Proceedings 4, pages 183-194. Springer, 1994. URL: https://doi.org/10.1007/3-540-58218-5_17.
  18. Mahdi Hashemi and Hassan A Karimi. A machine learning approach to improve the accuracy of gps-based map-matching algorithms. In 2016 IEEE 17th International Conference on Information Reuse and Integration (IRI), pages 77-86. IEEE, 2016. Google Scholar
  19. Gang Hu, Jie Shao, Fenglin Liu, Yuan Wang, and Heng Tao Shen. If-matching: Towards accurate map-matching with information fusion. IEEE Transactions on Knowledge and Data Engineering, 29(1):114-127, 2016. URL: https://doi.org/10.1109/TKDE.2016.2617326.
  20. Zhenfeng Huang, Shaojie Qiao, Nan Han, Chang-an Yuan, Xuejiang Song, and Yueqiang Xiao. Survey on vehicle map matching techniques. CAAI Transactions on Intelligence Technology, 6(1):55-71, 2021. URL: https://doi.org/10.1049/CIT2.12030.
  21. Georgios Kellaris, Nikos Pelekis, and Yannis Theodoridis. Map-matched trajectory compression. Journal of Systems and Software, 86(6):1566-1579, 2013. URL: https://doi.org/10.1016/J.JSS.2013.01.071.
  22. John Krumm, Eric Horvitz, and Julie Letchner. Map matching with travel time constraints. Technical report, SAE Technical Paper, 2007. Google Scholar
  23. Yin Lou, Chengyang Zhang, Yu Zheng, Xing Xie, Wei Wang, and Yan Huang. Map-matching for low-sampling-rate gps trajectories. In Proceedings of the 17th ACM SIGSPATIAL international conference on advances in geographic information systems, pages 352-361, 2009. URL: https://doi.org/10.1145/1653771.1653820.
  24. Reham Mohamed, Heba Aly, and Moustafa Youssef. Accurate real-time map matching for challenging environments. IEEE Transactions on Intelligent Transportation Systems, 18(4):847-857, 2016. URL: https://doi.org/10.1109/TITS.2016.2591958.
  25. Mark H Overmars, Haijo Schipper, and Micha Sharir. Storing line segments in partition trees. BIT Numerical Mathematics, 30(3):385-403, 1990. URL: https://doi.org/10.1007/BF01931656.
  26. Nagendra R Velaga. Development of a weight-based topological map-matching algorithm and an integrity method for location-based ITS services. PhD thesis, (C) Nagendra R. Velaga, 2010. Google Scholar
  27. Jan Vuurstaek, Glenn Cich, Luk Knapen, Wim Ectors, Tom Bellemans, Davy Janssens, et al. Gtfs bus stop mapping to the osm network. Future Generation Computer Systems, 110:393-406, 2020. URL: https://doi.org/10.1016/J.FUTURE.2018.02.020.
  28. Yuki Wakuda, Satoshi Asano, Noboru Koshizuka, and Ken Sakamura. An adaptive map-matching based on dynamic time warping for pedestrian positioning using network map. In Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium, pages 590-597. IEEE, 2012. Google Scholar
  29. Hong Wei, Yin Wang, George Forman, and Yanmin Zhu. Map matching by fréchet distance and global weight optimization. Technical Paper, Departement of Computer Science and Engineering, 19, 2013. Google Scholar
  30. Christopher E White, David Bernstein, and Alain L Kornhauser. Some map matching algorithms for personal navigation assistants. Transportation research part c: emerging technologies, 8(1-6):91-108, 2000. Google Scholar
  31. Kai Zhao, Jie Feng, Zhao Xu, Tong Xia, Lin Chen, Funing Sun, Diansheng Guo, Depeng Jin, and Yong Li. Deepmm: Deep learning based map matching with data augmentation. In Proceedings of the 27th ACM SIGSPATIAL international conference on advances in geographic information systems, pages 452-455, 2019. URL: https://doi.org/10.1145/3347146.3359090.
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