Scandinavian Thins on Top of Cake: On the Smallest One-Size-Fits-All Box

摘要

We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure.