Finding Optimal Solutions to Rubik's Cube Using Pattern Databases (1997) [87 citations — 5 self]
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author = {Richard E. Korf},
title = {Finding Optimal Solutions to Rubik's Cube Using Pattern Databases},
booktitle = {},
year = {1997},
pages = {700--705}
}
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Abstract:
We have found the first optimal solutions to random instances of Rubik's Cube. The median optimal solution length appears to be 18 moves. The algorithm used is iterative-deepening-A* (IDA*), with a lowerbound heuristic function based on large memory-based lookup tables, or "pattern databases" (Culberson and Schaeffer 1996). These tables store the exact number of moves required to solve various subgoals of the problem, in this case subsets of the individual movable cubies. We characterize the effectiveness of an admissible heuristic function by its expected value, and hypothesize that the overall performance of the program obeys a relation in which the product of the time and space used equals the size of the state space. Thus, the speed of the program increases linearly with the amount of memory available. As computer memories become larger and cheaper, we believe that this approach will become increasingly cost-effective. Introduction 1 Rubik's Cube, invented in the late 1970s by Ern...
Citations
| 122 | Macro-operators: A Weak Method for Learning – Korf - 1985 |
| 80 | A world championship caliber checkers program – Schaeffer, Culberson, et al. - 1992 |
| 39 | Searching with pattern databases – Culberson, Schaeffer - 1996 |
| 18 | BIDA*: An improved perimeter search algorithm – Manzini - 1995 |
| 16 | Machine discovery of effective admissible heuristics – Prieditis - 1993 |
| 11 | How to Use Limited Memory in Heuristic Search – Kaindl, Kainz, et al. - 1995 |
| 6 | Perimeter search – Dillenburg, Nelson - 1994 |
| 5 | Exploiting algebraic structure in parallel state space search – Bright, Kasif, et al. - 1994 |
| 5 | Planning and learning in permutation groups – Fiat, Moses, et al. - 1989 |
| 1 | Shamir's method on the super-flip, posting to Cube-Lovers mailing list – Moews |
