License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.51
URN: urn:nbn:de:0030-drops-160596
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16059/
Kim, Mincheol ;
Seo, Chanyang ;
Ahn, Taehoon ;
Ahn, Hee-Kap
Farthest-Point Voronoi Diagrams in the Presence of Rectangular Obstacles
Abstract
We present an algorithm to compute the geodesic L₁ farthest-point Voronoi diagram of m point sites in the presence of n rectangular obstacles in the plane. It takes O(nm+n log n + mlog m) construction time using O(nm) space. This is the first optimal algorithm for constructing the farthest-point Voronoi diagram in the presence of obstacles. We can construct a data structure in the same construction time and space that answers a farthest-neighbor query in O(log(n+m)) time.
BibTeX - Entry
@InProceedings{kim_et_al:LIPIcs.SoCG.2022.51,
author = {Kim, Mincheol and Seo, Chanyang and Ahn, Taehoon and Ahn, Hee-Kap},
title = {{Farthest-Point Voronoi Diagrams in the Presence of Rectangular Obstacles}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {51:1--51:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-227-3},
ISSN = {1868-8969},
year = {2022},
volume = {224},
editor = {Goaoc, Xavier and Kerber, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16059},
URN = {urn:nbn:de:0030-drops-160596},
doi = {10.4230/LIPIcs.SoCG.2022.51},
annote = {Keywords: Geodesic distance, L₁ metric, farthest-point Voronoi diagram}
}
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Keywords: |
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Geodesic distance, L₁ metric, farthest-point Voronoi diagram |
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Collection: |
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38th International Symposium on Computational Geometry (SoCG 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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01.06.2022 |
