From:

Subject:

On 01/05/95 at 17:12:18 mreid@ptc.com said:

for much too long now, i've meant to implement kociemba's algorithm

for quarter turns. finally i've gotten around to it, and it's foundsuperflip: B3 L3 U3 L3 F1 U1 D1 L3 B1 U1 F1 R3 L1 F3 B2 U1 D1 F2 B2 R2 U1 D1 26q

I read the articles in the archives about Kociemba's algorithm about

a year ago, without (I confess) fully understanding them. In particular,

I do not fully understand what differentiates Kociemba's algorithm from

Thistlethwaite's algorithm, other than it uses a different arrangement

of nested subgroups. I shall strive to read the articles again with

a deeper level of understanding.

But in the meantime, I wonder if you could verify that Kociemba's

algorithm does not guarantee to find a minimal process? In particular,

is it the case that 26q is a minimal superflip, or is it only an

upper bound?

The reason I ask is that I have decided to go ahead and calculate God's

Algorithm under quarter turns for depth 11. (Through depth 10 is

already in hand.) Once that is accomplished, it should be a

*fairly* easy task to establish a lower bound on the superflip

at 22 quarter turns via two half depth searches. In fact, the

second half depth search should be fairly easy to accomplish

because all I have to do is superflip each element of the data base

from the first search to establish the data base for the second

search.

I can already establish a lower bound of 14 quarter turns on the

superflip. It may be recalled that I was able to accomplish a

complete search for edges-only (no corners, no Face centers, and

rotations considered equivalent). There was some consternation

when I reported that the superflip was 9 quarter turns from Start

because the superflip is even. But without Face centers and with

rotations considered equivalent, normal parity rules do not

apply.

I am now working on edges-only, either with centers, or else with

rotations *not* considered equivalent (either G[E,F] or G[E]),

depending on which way you want to think about it.

In this case, the superflip really is even. I am working on level

13, and the superflip has not yet appeared. Hence, it is at least

at level 14 (without corners), and will therefore be at least at level

14 when the corners are added in. Strictly speaking, the superflip

has appeared already, and at level 9 just where it had to appear.

But in its appearance at level 9, it is composed with a non-trivial

rotation, so it isn't the superflip as the superflip is normally

understood.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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