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Japanese Conference on Discrete and Computational Geometry

JCDCG 2000: Discrete and Computational Geometry pp 67–80Cite as

Packing Convex Polygons into Rectangular Boxes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

Abstract

We consider the problem of packing several convex polygons into minimu, size rectangles. For this purpose the purpose the polygons may be moved either by translation only, or by combinations of translations and rotations. We investigates both cases, that the polygons may overlap when being packed or that they must be disjoint. The size of a rectangle to be minimized can either be its area or its perimeter. In the case of overlapping packing very efficient algorithms whose runtime is close to linear or O (n log n) can be found even for an arbitrary number of polygons. Disjoint optimal packing is known to be NP-hard for arbitrary numbers of polygons. Here, efficient algorithms are given for disjoint packing of two polygons with a runtime close to linear for translations and O (n 3) for general isometries.

Partially supported by the German Research Association (DFG), projects A1 253/4-2 and A1 253/4-3.

Partially supported by CUR Gen. Cat. 1999SGR00356 and Proyecto DGES-MEC PB98-0933.

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References

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Author information

Authors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takustr. 9, D-14195, Berlin

    Helmut Alt

  2. Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028, Barcelona, España

    Ferran Hurtado

Authors
  1. Helmut Alt
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  2. Ferran Hurtado
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Alt, H., Hurtado, F. (2001). Packing Convex Polygons into Rectangular Boxes. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_5

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  • DOI: https://doi.org/10.1007/3-540-47738-1_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

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