Solving the Rubik's Cube Optimally is NP-complete

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.

35 pages, 8 figures

Cited by in corpus (1)

• The Computational Complexity of Finding Hamiltonian Cycles in Grid Graphs of Semiregular Tessellations