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Maximum-Area Rectangles in a Simple Polygon

Authors: Yujin Choi, Seungjun Lee, and Hee-Kap Ahn

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)


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.

Cite as

Yujin Choi, Seungjun Lee, and Hee-Kap Ahn. Maximum-Area Rectangles in a Simple Polygon. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 12:1-12:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{choi_et_al:LIPIcs.FSTTCS.2019.12,
  author =	{Choi, Yujin and Lee, Seungjun and Ahn, Hee-Kap},
  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 =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.12},
  URN =		{urn:nbn:de:0030-drops-115745},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.12},
  annote =	{Keywords: Maximum-area rectangle, largest rectangle, simple polygon}
}
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