On Tue, 6 Feb 1996, Jerry Bryan wrote:

But here follows what I think is a new idea. What if we
formed all products XY for X in C[n] and Y in C[1]. Since
C[1] is Q, this is really just the procedure for a standard
depth first search. But we can't store C[n+1]. Can we
determine the size of C[n+1] anyway?

As is often the case, there is nothing new under the sun. I believe that
the "new" idea I was suggesting is very similar to, or perhaps identical
with, certain aspects (or all) of Shamir's algorithm. The best references
I have found in the archives are as follows:

Alan Bawden     27 May 87  Shamir's talk really was about how to 
                           solve the cube!

Michael Reid 16 Dec 94 Re: Cyclic Decomposition

David Moews 23 Jan 95 Shamir's method on the superflip

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Robert G. Bryan (Jerry Bryan)                jbryan@pstcc.cc.tn.us
Pellissippi State                            (423) 539-7127
10915 Hardin Valley Road                     (423) 694-6435 (fax)
P.O. Box 22990
Knoxville, TN 37933-0990