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.SoCG.2018.50
URN: urn:nbn:de:0030-drops-87639
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8763/
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Junginger, Kolja ; Papadopoulou, Evanthia

Deletion in Abstract Voronoi Diagrams in Expected Linear Time

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LIPIcs-SoCG-2018-50.pdf (1 MB)

Abstract

Updating an abstract Voronoi diagram in linear time, after deletion of one site, has been an open problem for a long time. Similarly for various concrete Voronoi diagrams of generalized sites, other than points. In this paper we present a simple, expected linear-time algorithm to update an abstract Voronoi diagram after deletion. We introduce the concept of a Voronoi-like diagram, a relaxed version of a Voronoi construct that has a structure similar to an abstract Voronoi diagram, without however being one. Voronoi-like diagrams serve as intermediate structures, which are considerably simpler to compute, thus, making an expected linear-time construction possible. We formalize the concept and prove that it is robust under an insertion operation, thus, enabling its use in incremental constructions.

BibTeX - Entry

@InProceedings{junginger_et_al:LIPIcs:2018:8763,
  author =	{Kolja Junginger and Evanthia Papadopoulou},
  title =	{{Deletion in Abstract Voronoi Diagrams in Expected Linear Time}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8763},
  URN =		{urn:nbn:de:0030-drops-87639},
  doi =		{10.4230/LIPIcs.SoCG.2018.50},
  annote =	{Keywords: Abstract Voronoi diagram, linear-time algorithm, update after deletion, randomized incremental algorithm}
}

Keywords: Abstract Voronoi diagram, linear-time algorithm, update after deletion, randomized incremental algorithm
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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