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.ESA.2020.45
URN: urn:nbn:de:0030-drops-129111
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12911/
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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
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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