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Map-Matching Queries Under Fréchet Distance on Low-Density Spanners

Authors Kevin Buchin , Maike Buchin , Joachim Gudmundsson , Aleksandr Popov , Sampson Wong

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LIPIcs.SoCG.2024.27.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Map Matching
  • Fréchet Distance
  • Data Structures

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Abstract

Map matching is a common task when analysing GPS tracks, such as vehicle trajectories. The goal is to match a recorded noisy polygonal curve to a path on the map, usually represented as a geometric graph. The Fréchet distance is a commonly used metric for curves, making it a natural fit. The map-matching problem is well-studied, yet until recently no-one tackled the data structure question: preprocess a given graph so that one can query the minimum Fréchet distance between all graph paths and a polygonal curve. Recently, Gudmundsson, Seybold, and Wong [Gudmundsson et al., 2023] studied this problem for arbitrary query polygonal curves and c-packed graphs. In this paper, we instead require the graphs to be λ-low-density t-spanners, which is significantly more representative of real-world networks. We also show how to report a path that minimises the distance efficiently rather than only returning the minimal distance, which was stated as an open problem in their paper.

Cite As Get BibTex

Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Aleksandr Popov, and Sampson Wong. Map-Matching Queries Under Fréchet Distance on Low-Density Spanners. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.27

Author Details

Kevin Buchin
  • Department of Computer Science, TU Dortmund, Germany
Maike Buchin
  • Faculty of Computer Science, Ruhr-Universität Bochum, Germany
Joachim Gudmundsson
  • School of Computer Science, University of Sydney, Australia
Aleksandr Popov
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Sampson Wong
  • Department of Computer Science, University of Copenhagen, Denmark

Funding

  • Popov, Aleksandr: Supported by the Dutch Research Council (NWO) under the project number 612.001.801.
  • Wong, Sampson: Supported in part by Starting Grant 1054-00032B from the Independent Research Fund Denmark under the Sapere Aude research career programme.

References

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