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Scandinavian Thins on Top of Cake: New and improved algorithms for stacking and packing
BibTeX
@MISC{Alt_scandinavianthins,
author = {Helmut Alt and Esther M. Arkin and Alon Efrat and George Hart and Ferran Hurtado and Irina Kostitsyna and Alexander Kröller and Joseph S. B. Mitchell and Valentin Polishchuk},
title = {Scandinavian Thins on Top of Cake: New and improved algorithms for stacking and packing},
year = {}
}
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Abstract
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. We also give efficient algorithms to find the smallest rectangle simultaneously enclosing a given pair of convex polygons.
