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.

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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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