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. © 2012 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Arkin, E. M., Efrat, A., Hart, G., Kostitsyna, I., Kröller, A., Mitchell, J. S. B., & Polishchuk, V. (2012). Scandinavian thins on top of cake: On the smallest one-size-fits-all box. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7288 LNCS, pp. 16–27). https://doi.org/10.1007/978-3-642-30347-0_5
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