Symmetric assembly puzzles are hard, beyond a few pieces

Erik D. Demaine, Matias Korman, Jason S. Ku, Joseph S.B. Mitchell, Yota Otachi, Andrévan Renssen, Marcel Roeloffzen, Ryuhei Uehara, Yushi Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publicationDiscrete and Computational Geometry and Graphs - 18th Japan Conference, JCDCGG 2015, Revised Selected Papers
EditorsToshinori Sakai, Hiro Ito, Jin Akiyama
PublisherSpringer-Verlag
Pages180-192
Number of pages13
ISBN (Print)9783319485317
DOIs
Publication statusPublished - 2016 Jan 1
Event18th Japan Conference on Discrete and Computational Geometry and Graphs, JCDCGG 2015 - Kyoto, Japan
Duration: 2015 Sep 142015 Sep 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9943 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th Japan Conference on Discrete and Computational Geometry and Graphs, JCDCGG 2015
CountryJapan
CityKyoto
Period15/9/1415/9/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Demaine, E. D., Korman, M., Ku, J. S., Mitchell, J. S. B., Otachi, Y., Renssen, A., Roeloffzen, M., Uehara, R., & Uno, Y. (2016). Symmetric assembly puzzles are hard, beyond a few pieces. In T. Sakai, H. Ito, & J. Akiyama (Eds.), Discrete and Computational Geometry and Graphs - 18th Japan Conference, JCDCGG 2015, Revised Selected Papers (pp. 180-192). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9943 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-48532-4_16