Extremal convex polygons inscribed in a given convex polygon

A convex polygon Q is inscribed in a convex polygon P if every side of P contains at least one vertex of Q. We present algorithms for finding a minimum area and a minimum perimeter convex polygon inscribed in any given convex n-gon in O(n) and O(n(3)) time, respectively. We also investigate other variants of this problem. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).