AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A comparative analysis of parallel disk-based Methods for enumerating implicit graphs
Proceedings of the 2007 international workshop on Parallel symbolic computation
Solving Rubik's Cube: disk is the new RAM
Communications of the ACM - The psychology of security: why do good users make bad decisions?
Linear-time disk-based implicit graph search
Journal of the ACM (JACM)
Proof Pearl: Revisiting the Mini-rubik in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Harnessing parallel disks to solve Rubik's cube
Journal of Symbolic Computation
Minimizing disk I/O in two-bit breadth-first search
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Perfect hashing for state spaces in BDD representation
KI'09 Proceedings of the 32nd annual German conference on Advances in artificial intelligence
Fast multiplication of large permutations for disk, flash memory and RAM
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Strongly solving fox-and-geese on multi-core CPU
KI'10 Proceedings of the 33rd annual German conference on Advances in artificial intelligence
An efficient programming model for memory-intensive recursive algorithms using parallel disks
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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The number of moves required to solve any state of Rubik's cube has been a matter of long-standing conjecture for over 25 years -- since Rubik's cube appeared. This number is sometimes called "God's number". An upper bound of 29 (in the face-turn metric) was produced in the early 1990's, followed by an upper bound of 27 in 2006. An improved upper bound of 26 is produced using 8000 CPU hours. One key to this result is a new, fast multiplication in the mathematical group of Rubik's cube. Another key is efficient out-of-core (disk-based) parallel computation using terabytes of disk storage. One can use the precomputed data structures to produce such solutions for a specific Rubik's cube position in a fraction of a second. Work in progress will use the new "brute-forcing" technique to further reduce the bound.