[next] [prev] [up] Date: Fri, 20 Jan 95 17:07:05 -0500 (EST)
[next] [prev] [up] From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
[next] [prev] [up] Subject: Re: superflip in quarter turn metric

On 01/20/95 at 15:58:08 mreid@ptc.com said:
>i've finished searching for superflip in 20q , and no solutions were
>found. thus superflip requires at least 22q , which gives a new lower
>bound for the diameter of the cube group in the quarter turn metric.
>total cpu spent on the search was 29 cpu hours. based on this, i would
>make a rough estimate of 2.5 to 3 months cpu time for an exhaustive
>search through depth 22q.

Rats. You beat me by about a half hour. I just finished comparing
Level 10 of my data base with the same Level 10 superflipped. There
were no matches.

I just about have Level 11 completed. This will provide interesting
new information in and of itself, because previously there has only
been an exhaustive search through level 10. Once I complete Level 11,
I will superflip it and see what happens.

The superflip is especially amenable to a "two half depth search".
Normally, you would have to build one tree with Start at the root,
and a second tree with X at the root, where X is the position you
were testing. But a search tree with superflip at the root is
identical to a search tree with Start at the root except that the
superflip tree has each element superflipped as compared to the
respective element of the tree with Start at the root. Hence,
building the tree with Superflip at the root is quite easy once
the tree with Start at the root is in hand.

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Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
Associate Director, WVNET                            (304) 293-5540 fax
837 Chestnut Ridge Road                              BRYAN@WVNVM
Morgantown, WV 26505                                 BRYAN@WVNVM.WVNET.EDU

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