Scandinavian thins on top of cake: on the smallest one-size-fits-all box

Authors:
Esther M. Arkin;Alon Efrat;George Hart;Irina Kostitsyna;Alexander Kröller;Joseph S. B. Mitchell;Valentin Polishchuk
Affiliations:
AMS Dept., Stony Brook University;CS Dept., The University of Arizona;The Museum of Mathematics;CS Dept., Stony Brook University;CS Dept., Technische Universität Braunschweig, Germany;AMS Dept., Stony Brook University;CS Dept., University of Helsinki, HIIT, Finland
Venue:
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Year:
2012

Citing 4
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Containment algorithms for objects in rectangular boxes

Theory and practice of geometric modeling
Faster core-set constructions and data stream algorithms in fixed dimensions

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points

Journal of the ACM (JACM)
Aligning Two Convex Figures to Minimize Area or Perimeter

Algorithmica

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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.