License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.17
URN: urn:nbn:de:0030-drops-104219
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10421/
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Bringmann, Karl ; Künnemann, Marvin ; Nusser, André

Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance

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LIPIcs-SoCG-2019-17.pdf (1 MB)

Abstract

The Fréchet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Fréchet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Fréchet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fréchet distance.
In this work, we present a fast, certifying implementation for deciding the Fréchet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure.

BibTeX - Entry

@InProceedings{bringmann_et_al:LIPIcs:2019:10421,
  author =	{Karl Bringmann and Marvin K{\"u}nnemann and Andr{\'e} Nusser},
  title =	{{Walking the Dog Fast in Practice: Algorithm Engineering of the Fr{\'e}chet Distance}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10421},
  URN =		{urn:nbn:de:0030-drops-104219},
  doi =		{10.4230/LIPIcs.SoCG.2019.17},
  annote =	{Keywords: curve simplification, Fr{\'e}chet distance, algorithm engineering}
}

Keywords: curve simplification, Fréchet distance, algorithm engineering
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019
Supplementary Material: https://github.com/chaot4/frechet_distance

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