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Matching Polygonal Curves with Respect to the Fréchet Distance

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

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Abstract

We provide the first algorithm for matching two polygonal curves P and Q under translations with respect to the Fréchet distance. If P and Q consist of m and n segments, respectively, the algorithm has runtime O((mn)3(m+n)2log(m+n)). We also present an algorithm giving an approximate solution as an alternative. To this end, we generalize the notion of a reference point and observe that all reference points for the Hausdorff distance are also reference points for the Fréchet distance. Furthermore we give a new reference point that is substantially better than all known reference points for the Hausdorff distance. These results yield a (1 + ∈)-approximation algorithm for the matching problem that has runtime O(∈-2 mn).

This research was supported by the Deutsche Forschungsgemeinschaft under Grant No. AL 253/4-3.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195, Berlin, Germany

    Helmut Alt, Christian Knauer & Carola Wenk

Authors
  1. Helmut Alt
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  2. Christian Knauer
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  3. Carola Wenk
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Alt, H., Knauer, C., Wenk, C. (2001). Matching Polygonal Curves with Respect to the Fréchet Distance. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_6

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  • DOI: https://doi.org/10.1007/3-540-44693-1_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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