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Box Pleating is Hard

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Discrete and Computational Geometry and Graphs (JCDCGG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9943))

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Abstract

Flat foldability of general crease patterns was first claimed to be hard for over twenty years. In this paper we prove that deciding flat foldability remains NP-complete even for box pleating, where creases form a subset of a square grid with diagonals. In addition, we provide new terminology to implicitly represent the global layer order of a flat folding, and present a new planar reduction framework for grid-aligned gadgets.

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Notes

  1. 1.

    This problem is sometimes called ‘positive’ as variables cannot appear negated within clauses, however we follow the naming convention from [Sch78].

References

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Acknowledgements

This work was begun at the 2015 Bellairs Workshop on Computational Geometry, co-organized by Erik Demaine and Godfried Toussaint. We thank the other participants of the workshop for stimulating discussions, and to Barry Hayes for helpful comments leading to some simplifications. The research of H. Akitaya was supported by NSF grant CCF-1422311 and Science without Borders. The research of T. Hull and T. Tachi were respectively supported by NSF grant EFRI-ODISSEI-1240441 and the JST Presto Program.

Author information

Authors and Affiliations

  1. Tufts University, Medford, USA

    Hugo A. Akitaya

  2. NASA, Washington, D.C., USA

    Kenneth C. Cheung

  3. MIT, Cambridge, USA

    Erik D. Demaine & Jason S. Ku

  4. Saitama University, Saitama, Japan

    Takashi Horiyama

  5. Western New England University, Springfield, USA

    Thomas C. Hull

  6. The University of Tokyo, Tokyo, Japan

    Tomohiro Tachi

  7. JAIST, Nomi, Japan

    Ryuhei Uehara

Authors
  1. Hugo A. Akitaya
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  2. Kenneth C. Cheung
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  3. Erik D. Demaine
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  4. Takashi Horiyama
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  5. Thomas C. Hull
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  6. Jason S. Ku
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  7. Tomohiro Tachi
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  8. Ryuhei Uehara
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Corresponding author

Correspondence to Hugo A. Akitaya .

Editor information

Editors and Affiliations

  1. Tokyo University of Science , Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications , Tokyo, Japan

    Hiro Ito

  3. Tokai University , Tokyo, Japan

    Toshinori Sakai

  4. Osaka Prefecture University , Sakai, Japan

    Yushi Uno

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Akitaya, H.A. et al. (2016). Box Pleating is Hard. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-48532-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48531-7

  • Online ISBN: 978-3-319-48532-4

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