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.
Keywords
- Convex Polygon
- Simple Polygon
- Lower Envelope
- Small Rectangle
- Variable Item
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2012 Springer-Verlag Berlin Heidelberg
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Arkin, E.M. et al. (2012). Scandinavian Thins on Top of Cake: On the Smallest One-Size-Fits-All Box. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_5
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DOI: https://doi.org/10.1007/978-3-642-30347-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30346-3
Online ISBN: 978-3-642-30347-0
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