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Aug 15, 2013 at 9:11 comment added Stefan Kohl Thanks for the reference. -- Though I don't see that the paper answers the question. The author derives bounds on the diameter of certain Cayley graphs, shows that they are sharp and says that the naive way to evaluate the bounds takes $n!$ times a polynomial operations. Though I have not read everything in full.
Aug 14, 2013 at 23:24 history answered Igor Rivin CC BY-SA 3.0