Bundling three convex polygons to minimize area or perimeter

Abstract

Given three convex polygons having n vertices in total in the plane, we consider the problem of finding a translation for each polygon such that the translated polygons are pairwise disjoint and the area or the perimeter of their convex hull is minimized. We present the first O(n(2))-time algorithm that finds optimal translations of input polygons using O(n(2)) space for this problem. (C) 2015 Elsevier B.V. All rights reserved.