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

Research output: Contribution to journalArticlepeer-review


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
Article number101648
JournalComputational Geometry: Theory and Applications
Publication statusPublished - 2020 Oct


  • Assembly puzzle
  • NP-complete
  • Parameterized algorithms

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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