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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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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.

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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.

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