License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2019.12
URN: urn:nbn:de:0030-drops-115745
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11574/
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Choi, Yujin ; Lee, Seungjun ; Ahn, Hee-Kap

Maximum-Area Rectangles in a Simple Polygon

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LIPIcs-FSTTCS-2019-12.pdf (0.6 MB)

Abstract

We study the problem of finding maximum-area rectangles contained in a polygon in the plane. There has been a fair amount of work for this problem when the rectangles have to be axis-aligned or when the polygon is convex. We consider this problem in a simple polygon with n vertices, possibly with holes, and with no restriction on the orientation of the rectangles. We present an algorithm that computes a maximum-area rectangle in O(n^3 log n) time using O(kn^2) space, where k is the number of reflex vertices of P. Our algorithm can report all maximum-area rectangles in the same time using O(n^3) space. We also present a simple algorithm that finds a maximum-area rectangle contained in a convex polygon with n vertices in O(n^3) time using O(n) space.

BibTeX - Entry

@InProceedings{choi_et_al:LIPIcs:2019:11574,
  author =	{Yujin Choi and Seungjun Lee and Hee-Kap Ahn},
  title =	{{Maximum-Area Rectangles in a Simple Polygon}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11574},
  URN =		{urn:nbn:de:0030-drops-115745},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.12},
  annote =	{Keywords: Maximum-area rectangle, largest rectangle, simple polygon}
}

Keywords: Maximum-area rectangle, largest rectangle, simple polygon
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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