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

arXiv · 1703.02671

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

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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.

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Erik D. Demaine, Matias Korman, Jason S. Ku, Joseph S. B. Mitchell, Yota Otachi, André van Renssen, Marcel Roeloffzen, Ryuhei Uehara, Yushi Uno. 2017-03-08. Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces. https://arxiv.org/abs/1703.02671

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