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.ISAAC.2020.28
URN: urn:nbn:de:0030-drops-133725
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13372/
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Funke, Stefan ; Weitbrecht, Felix

Efficiently Computing All Delaunay Triangles Occurring over All Contiguous Subsequences

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LIPIcs-ISAAC-2020-28.pdf (0.8 MB)

Abstract

Given an ordered sequence of points P = {p₁, p₂, … , p_n}, we are interested in computing T, the set of distinct triangles occurring over all Delaunay triangulations of contiguous subsequences within P. We present a deterministic algorithm for this purpose with near-optimal time complexity O(|T|log n). Additionally, we prove that for an arbitrary point set in random order, the expected number of Delaunay triangles occurring over all contiguous subsequences is Θ(nlog n).

BibTeX - Entry

@InProceedings{funke_et_al:LIPIcs:2020:13372,
  author =	{Stefan Funke and Felix Weitbrecht},
  title =	{{Efficiently Computing All Delaunay Triangles Occurring over All Contiguous Subsequences}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13372},
  URN =		{urn:nbn:de:0030-drops-133725},
  doi =		{10.4230/LIPIcs.ISAAC.2020.28},
  annote =	{Keywords: Computational Geometry, Delaunay Triangulation, Randomized Analysis}
}

Keywords: Computational Geometry, Delaunay Triangulation, Randomized Analysis
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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