Bundling three convex polygons to minimize area or perimeter

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(n2)O(n2)-time algorithm that finds optimal translations of input polygons using O(n2)O(n2) space for this problem.