Algorithms for solving Rubik's cubes
ESA'11 Proceedings of the 19th European conference on Algorithms
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We show that any group represented by generators that are cycles of bounded degree has O(n2) diameter, i.e., that the longest product of generators required to reach any permutation in the group is O(n2). We also show how such “short” products can be found in polynomial time. The techniques presented are applicable to generalizations of many permutation-group puzzles such as Alexander's Star and the Hungarian Rings.