Solving the Rubik’s Cube optimally is NP-complete
Name
LIPIcs-STACS-2018-24.pdf
Description
Published version
Size
661.82 KB
Format
Adobe PDF
Checksum (MD5)
1664c61dfad921976da1899121a2276a
Author(s)
Demaine, Erik D
Eisenstat, Sarah Charmian
Rudoy, Mikhail
Date Issued
2018
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.STACS.2018.24
