Solving the Rubik's Cube Optimally is NP-complete

Erik D. Demaine; Sarah Eisenstat; Mikhail Rudoy

doi:10.4230/lipics.stacs.2018.24

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arXiv · 1706.06708

Solving the Rubik's Cube Optimally is NP-complete

Erik D. Demaine·Sarah Eisenstat·Mikhail Rudoy

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Abstract

In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an $n \times n \times n$ Rubik's Cube with missing stickers is NP-complete. We prove this result first for the simpler case of the Rubik's Square---an $n \times n \times 1$ generalization of the Rubik's Cube---and then proceed with a similar but more complicated proof for the Rubik's Cube case.

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BibTeX RIS

Erik D. Demaine, Sarah Eisenstat, Mikhail Rudoy. 2018-04-27. Solving the Rubik's Cube Optimally is NP-complete. https://doi.org/10.4230/lipics.stacs.2018.24

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