Computational Complexity of Piano-Hinged Dissections

Zachary ABEL; Erik D. DEMAINE; Martin L. DEMAINE; Takashi HORIYAMA; Ryuhei UEHARA

doi:10.1587/transfun.E97.A.1206

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Special Section on Discrete Mathematics and Its Applications

Computational Complexity of Piano-Hinged Dissections

Zachary ABEL, Erik D. DEMAINE, Martin L. DEMAINE, Takashi HORIYAMA, Ryuhei UEHARA

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Keywords: GeoLoop, hinged dissection, Ivan's Hinge, NP-hardness, paper folding

JOURNAL RESTRICTED ACCESS

2014 Volume E97.A Issue 6 Pages 1206-1212

DOI https://doi.org/10.1587/transfun.E97.A.1206

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Abstract

We prove NP-completeness of deciding whether a given loop of colored right isosceles triangles, hinged together at edges, can be folded into a specified rectangular three-color pattern. By contrast, the same problem becomes polynomially solvable with one color or when the target shape is a tree-shaped polyomino.

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