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DOI: 10.4230/LIPIcs.ESA.2020.45
URN: urn:nbn:de:0030-drops-129111
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12911/
Fan, Chenglin ; Raichel, Benjamin
Linear Expected Complexity for Directional and Multiplicative Voronoi Diagrams
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Abstract
While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi Voronoi diagrams. These diagrams both have quadratic worst-case complexity, though here we show that their expected complexity is linear for certain natural randomized inputs. Specifically, we argue that the expected complexity is linear for: (1) semi Voronoi diagrams when the visible direction is randomly sampled, and (2) for multiplicative diagrams when either weights are sampled from a constant-sized set, or the more challenging case when weights are arbitrary but locations are sampled from a square.
BibTeX - Entry
@InProceedings{fan_et_al:LIPIcs:2020:12911,
author = {Chenglin Fan and Benjamin Raichel},
title = {{Linear Expected Complexity for Directional and Multiplicative Voronoi Diagrams}},
booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)},
pages = {45:1--45:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-162-7},
ISSN = {1868-8969},
year = {2020},
volume = {173},
editor = {Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12911},
URN = {urn:nbn:de:0030-drops-129111},
doi = {10.4230/LIPIcs.ESA.2020.45},
annote = {Keywords: Voronoi Diagrams, Expected Complexity, Computational Geometry}
}
| Keywords: | Voronoi Diagrams, Expected Complexity, Computational Geometry | |
| Seminar: | 28th Annual European Symposium on Algorithms (ESA 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 26.08.2020 |
