Solving the Rubik’s Cube optimally is NP-complete
Author(s)
Demaine, Erik D; Eisenstat, Sarah Charmian; Rudoy, Mikhail
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In this paper, we prove that optimally solving an n × n × 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×n×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 × n × 1 generalization of the Rubik’s Cube - and then proceed with a similar but more complicated proof for the Rubik’s Cube case. Our results hold both when the goal is make the sides monochromatic and when the goal is to put each sticker into a specific location.
Date issued
2018Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence LaboratoryJournal
Leibniz International Proceedings in Informatics
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Citation
Demaine, Erik D., et al. “Solving the Rubik’s Cube Optimally Is NP-Complete.” Leibniz International Proceedings in Informatics 96 (2018): n. pag. © Erik D. Demaine, Sarah Eisenstat, and Mikhail Rudoy
Version: Final published version
ISSN
1868-8969