Maximum-Area Rectangles in a Simple Polygon

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.