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**1 - 1**of**1**### Finding Largest Rectangles in Convex Polygons

, 2014

"... We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n3). We also give (1 − ε)-approximation algorithms that take tim ..."

Abstract
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We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n3). We also give (1 − ε)-approximation algorithms that take time O(ε−3/2 +ε−1/2 logn) for maximizing the area and O(ε−3 +ε−1 logn) for maximizing the perimeter.