eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-12-04
12:1
12:14
10.4230/LIPIcs.FSTTCS.2019.12
article
Maximum-Area Rectangles in a Simple Polygon
Choi, Yujin
1
Lee, Seungjun
2
Ahn, Hee-Kap
2
https://orcid.org/0000-0001-7177-1679
Technische Universität Berlin, Germany
Pohang University of Science and Technology, Pohang, Korea
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol150-fsttcs2019/LIPIcs.FSTTCS.2019.12/LIPIcs.FSTTCS.2019.12.pdf
Maximum-area rectangle
largest rectangle
simple polygon