Symmetric assembly puzzles are hard, beyond a few pieces

Author(s)
Demaine, Erik D; Ku, Jason S
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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.
Date issued
2020-10
URI
https://hdl.handle.net/1721.1/128811
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Computational Geometry: Theory and Applications
Publisher
Elsevier BV
Citation
Demaine, Erik D. et al. “Symmetric assembly puzzles are hard, beyond a few pieces.” Computer methods in applied mechanics and engineering, 90 (October 2020): 101648 © 2020 The Author(s)
Version: Original manuscript
ISSN
0925-7721
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