Harnessing parallel disks to solve Rubik's cube

Authors:
Daniel Kunkle;Gene Cooperman
Affiliations:
College of Computer Science, Northeastern University, Boston, MA 02115, USA;College of Computer Science, Northeastern University, Boston, MA 02115, USA
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

The number of moves required to solve any configuration of Rubik's cube has held a fascination for over 25 years. A new upper bound of 26 is produced. More important, a new methodology is described for finding upper bounds. The novelty is two-fold. First, parallel disks are employed. This allows 1.4x10^1^2 states representing symmetrized cosets to be enumerated in seven terabytes. Second, a faster table-based multiplication is described for symmetrized cosets that attempts to keep most tables in the CPU cache. This enables the product of a symmetrized coset by a generator at a rate of 10 million moves per second.