Scandinavian thins on top of cake: New and improved algorithms for stacking and packing

Helmut Alt, Esther M. Arkin, Alon Efrat, George Hart, Ferran Hurtado, Irina Kostitsyna, Alexander Kröller, Joseph S.B. Mitchell, Valentin Polishchuk

Research output: Contribution to journalArticle

1 Scopus citations

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 forthe 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.

Original languageEnglish (US)
Pages (from-to)689-714
Number of pages26
JournalTheory of Computing Systems
Volume54
Issue number4
DOIs
StatePublished - 2014

Keywords

  • Computational geometry
  • Enclosure
  • Packing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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    Alt, H., Arkin, E. M., Efrat, A., Hart, G., Hurtado, F., Kostitsyna, I., Kröller, A., Mitchell, J. S. B., & Polishchuk, V. (2014). Scandinavian thins on top of cake: New and improved algorithms for stacking and packing. Theory of Computing Systems, 54(4), 689-714. https://doi.org/10.1007/s00224-013-9493-9