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.FSTTCS.2021.19
URN: urn:nbn:de:0030-drops-155300
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15530/
Eom, Taekang ;
Lee, Seungjun ;
Ahn, Hee-Kap
Largest Similar Copies of Convex Polygons in Polygonal Domains
Abstract
Given a convex polygon with k vertices and a polygonal domain consisting of polygonal obstacles with n vertices in total in the plane, we study the optimization problem of finding a largest similar copy of the polygon that can be placed in the polygonal domain without intersecting the obstacles. We present an upper bound O(k²n²λ₄(k)) on the number of combinatorial changes occurred to the underlying structure during the rotation of the polygon, together with an O(k²n²λ₄(k)log n)-time deterministic algorithm for the problem. This improves upon the previously best known results by Chew and Kedem [SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more than 27 years. Our result also improves the time complexity of the high-clearance motion planning algorithm by Chew and Kedem.
BibTeX - Entry
@InProceedings{eom_et_al:LIPIcs.FSTTCS.2021.19,
author = {Eom, Taekang and Lee, Seungjun and Ahn, Hee-Kap},
title = {{Largest Similar Copies of Convex Polygons in Polygonal Domains}},
booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
pages = {19:1--19:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-215-0},
ISSN = {1868-8969},
year = {2021},
volume = {213},
editor = {Boja\'{n}czy, Miko{\l}aj and Chekuri, Chandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15530},
URN = {urn:nbn:de:0030-drops-155300},
doi = {10.4230/LIPIcs.FSTTCS.2021.19},
annote = {Keywords: Polygon placement, Largest similar copy, Polygonal domain}
}
Keywords: |
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Polygon placement, Largest similar copy, Polygonal domain |
Collection: |
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41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021) |
Issue Date: |
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2021 |
Date of publication: |
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29.11.2021 |