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

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7288)

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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References

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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

  • eBook Packages: Computer ScienceComputer Science (R0)