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DOI: 10.4230/LIPIcs.SoCG.2018.50
URN: urn:nbn:de:0030-drops-87639
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8763/
Junginger, Kolja ; Papadopoulou, Evanthia
Deletion in Abstract Voronoi Diagrams in Expected Linear Time
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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 | |
| Seminar: | 34th International Symposium on Computational Geometry (SoCG 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 08.06.2018 |
