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

  • Esther M. Arkin
  • Alon Efrat
  • George Hart
  • Irina Kostitsyna
  • Alexander Kröller
  • Joseph S. B. Mitchell
  • Valentin Polishchuk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


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.


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Esther M. Arkin
    • 1
  • Alon Efrat
    • 2
  • George Hart
    • 3
  • Irina Kostitsyna
    • 4
  • Alexander Kröller
    • 5
  • Joseph S. B. Mitchell
    • 1
  • Valentin Polishchuk
    • 6
  1. 1.AMS Dept.Stony Brook UniversityUSA
  2. 2.CS Dept.The University of ArizonaUSA
  3. 3.The Museum of MathematicsUSA
  4. 4.CS Dept.Stony Brook UniversityUSA
  5. 5.CS Dept.Technische Universität BraunschweigGermany
  6. 6.CS Dept.University of Helsinki, HIITFinland

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