Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces

  • Erik D. Demaine
  • Matias Korman
  • Jason S. Ku
  • Joseph S. B. Mitchell
  • Yota Otachi
  • André van Renssen
  • Marcel Roeloffzen
  • Ryuhei Uehara
  • Yushi Uno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9943)

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.

Notes

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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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Matias Korman
    • 2
  • Jason S. Ku
    • 1
  • Joseph S. B. Mitchell
    • 3
  • Yota Otachi
    • 4
  • André van Renssen
    • 5
    • 6
  • Marcel Roeloffzen
    • 5
    • 6
  • Ryuhei Uehara
    • 4
  • Yushi Uno
    • 7
  1. 1.MITCambridgeUSA
  2. 2.Tohoku UniversitySendaiJapan
  3. 3.Stony Brook UniversityStony BrookUSA
  4. 4.JAISTNomiJapan
  5. 5.National Institute of InformaticsTokyoJapan
  6. 6.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan
  7. 7.Osaka Prefecture UniversitySakaiJapan

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