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DOI: 10.4230/LIPIcs.ESA.2019.67
URN: urn:nbn:de:0030-drops-111887
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11188/
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van de Kerkhof, Mees ; Kostitsyna, Irina ; Löffler, Maarten ; Mirzanezhad, Majid ; Wenk, Carola

Global Curve Simplification

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LIPIcs-ESA-2019-67.pdf (0.8 MB)


Abstract

Due to its many applications, curve simplification is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve P with n vertices, the goal is to find another polygonal curve P' with a smaller number of vertices such that P' is sufficiently similar to P. Quality guarantees of a simplification are usually given in a local sense, bounding the distance between a shortcut and its corresponding section of the curve. In this work we aim to provide a systematic overview of curve simplification problems under global distance measures that bound the distance between P and P'. We consider six different curve distance measures: three variants of the Hausdorff distance and three variants of the Fréchet distance. And we study different restrictions on the choice of vertices for P'. We provide polynomial-time algorithms for some variants of the global curve simplification problem, and show NP-hardness for other variants. Through this systematic study we observe, for the first time, some surprising patterns, and suggest directions for future research in this important area.

BibTeX - Entry

@InProceedings{vandekerkhof_et_al:LIPIcs:2019:11188,
  author =	{Mees van de Kerkhof and Irina Kostitsyna and Maarten L{\"o}ffler and Majid Mirzanezhad and Carola Wenk},
  title =	{{Global Curve Simplification}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11188},
  URN =		{urn:nbn:de:0030-drops-111887},
  doi =		{10.4230/LIPIcs.ESA.2019.67},
  annote =	{Keywords: Curve simplification, Fr{\'e}chet distance, Hausdorff distance}
}

Keywords: Curve simplification, Fréchet distance, Hausdorff distance
Seminar: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019


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