2026-08-16T15:54:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11574 2024-03-06T10:48:21Z ddc:004 open_access

Maximum-Area Rectangles in a Simple Polygon Choi, Yujin Lee, Seungjun Ahn, Hee-Kap Maximum-area rectangle largest rectangle simple polygon 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yujin Choi and Seungjun Lee and Hee-Kap Ahn 2019 Is Part Of LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2019.12 urn:nbn:de:0030-drops-115745 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.12 eng https://creativecommons.org/licenses/by/3.0/legalcode