Approximation of Convex Figures by Pairs of Rectangles

We consider the problem of approximating a convex gure in the plane by a pair (r; R) of homothetic (that is, similar and parallel) rectangles with r  C  R. We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle, thereby solving a problem posed by Polya and Szeg}o. If the n vertices of a convex polygon C are given as a sorted array, such an approximating pair of rectangles can be computed in time O(log2 n).

• Type: Conference
• Year: 1990
• Where: STACS
• Authors: Otfried Schwarzkopf, Ulrich Fuchs, Günter Rote, Emo Welzl
• Keywords: Convex Gure, Outer Rectangle, Rectangles, STACS 1990, Theoretical Computer Science