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DOI: 10.4230/LIPIcs.SoCG.2021.59
URN: urn:nbn:de:0030-drops-138585
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13858/
Wang, Haitao
An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons
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Abstract
Given a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P. It is known that the problem has an Ω(n+mlog m) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that can solve the problem in O(n+mlog m) expected time. The previous best deterministic algorithms solve the problem in O(nlog log n+ mlog m) time [Oh, Barba, and Ahn, SoCG 2016] or in O(n+mlog m+mlog² n) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm of O(n+mlog m) time, which is optimal. This answers an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.
BibTeX - Entry
@InProceedings{wang:LIPIcs.SoCG.2021.59,
author = {Wang, Haitao},
title = {{An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons}},
booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)},
pages = {59:1--59:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-184-9},
ISSN = {1868-8969},
year = {2021},
volume = {189},
editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13858},
URN = {urn:nbn:de:0030-drops-138585},
doi = {10.4230/LIPIcs.SoCG.2021.59},
annote = {Keywords: farthest-sites, Voronoi diagrams, triple-point geodesic center, simple polygons}
}
| Keywords: | farthest-sites, Voronoi diagrams, triple-point geodesic center, simple polygons | |
| Seminar: | 37th International Symposium on Computational Geometry (SoCG 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 02.06.2021 |
