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/
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Eom, Taekang ; Lee, Seungjun ; Ahn, Hee-Kap

Largest Similar Copies of Convex Polygons in Polygonal Domains

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LIPIcs-FSTTCS-2021-19.pdf (1.0 MB)

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: Polygon placement, Largest similar copy, Polygonal domain
Collection: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Issue Date: 2021
Date of publication: 29.11.2021

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