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Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces

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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

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant.

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Acknowledgements

Many of the authors were introduced to symmetric assembly puzzles during the 30th Winter Workshop on Computational Geometry at the Bellairs Research Institute of McGill University, March 2015. Korman is supported in part by the ELC project (MEXT KAKENHI No. 24106008). Mitchell is supported in part by the National Science Foundation (CCF-1526406). Uno is supported in part by the ELC project (MEXT KAKENHI No. 15H00853).

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Authors and Affiliations

  1. MIT, Cambridge, USA

    Erik D. Demaine & Jason S. Ku

  2. Tohoku University, Sendai, Japan

    Matias Korman

  3. Stony Brook University, Stony Brook, USA

    Joseph S. B. Mitchell

  4. JAIST, Nomi, Japan

    Yota Otachi & Ryuhei Uehara

  5. National Institute of Informatics, Tokyo, Japan

    André van Renssen & Marcel Roeloffzen

  6. JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

    André van Renssen & Marcel Roeloffzen

  7. Osaka Prefecture University, Sakai, Japan

    Yushi Uno

Authors
  1. Erik D. Demaine
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  2. Matias Korman
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  3. Jason S. Ku
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  4. Joseph S. B. Mitchell
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  5. Yota Otachi
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  6. André van Renssen
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  7. Marcel Roeloffzen
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  8. Ryuhei Uehara
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  9. Yushi Uno
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Corresponding author

Correspondence to Jason S. Ku .

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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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Demaine, E.D. et al. (2016). Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces. 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_16

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  • DOI: https://doi.org/10.1007/978-3-319-48532-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48531-7

  • Online ISBN: 978-3-319-48532-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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