Algorithms for Solving Rubik's Cubes

@article{Demaine2011AlgorithmsFS,
  title={Algorithms for Solving Rubik's Cubes},
  author={Erik D. Demaine and Martin L. Demaine and Sarah Eisenstat and Anna Lubiw and Andrew Winslow},
  journal={ArXiv},
  year={2011},
  volume={abs/1106.5736}
}
The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic structure. Specifically, we show that the n×n×n Rubik's Cube, as well as the n×n× 1 variant, has a "God's Number" (diameter of the configuration space) of Θ(n2/ log n). The upper bound comes from effectively parallelizing standard Θ(n2) solution algorithms, while the… 
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