From BRYAN@wvnvm.wvnet.edu Sun Jan 8 23:24:08 1995 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA27846; Sun, 8 Jan 95 23:24:08 EST Message-Id: <9501090424.AA27846@life.ai.mit.edu> Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 7702; Sun, 08 Jan 95 23:16:57 EST Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 9435; Sun, 8 Jan 1995 23:16:57 -0500 X-Acknowledge-To: Date: Sun, 8 Jan 1995 23:16:52 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: kociemba's algorithm for quarter turns In-Reply-To: Message of 01/05/95 at 17:12:18 from mreid@ptc.com 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 found >superflip: > 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