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DOI: 10.4230/LIPIcs.ISAAC.2020.28
URN: urn:nbn:de:0030-drops-133725
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13372/
Funke, Stefan ; Weitbrecht, Felix
Efficiently Computing All Delaunay Triangles Occurring over All Contiguous Subsequences
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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 | |
| Seminar: | 31st International Symposium on Algorithms and Computation (ISAAC 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
