From @mitvma.mit.edu:hans@freyr.research.ptt.nl Fri May 29 13:21:10 1992 Return-Path: <@mitvma.mit.edu:hans@freyr.research.ptt.nl> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) id AA09766; Fri, 29 May 92 13:21:10 EDT Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 3176; Fri, 29 May 92 13:22:18 EDT Received: from research.ptt.nl by MITVMA.MIT.EDU (Mailer R2.08 R208004) with BSMTP id 8330; Fri, 29 May 92 13:22:17 EDT Received: from dnlunx.research.ptt.nl (DNLUNX) by research.ptt.nl (PMDF #12085) id <01GKLFC81PO0DQGQ2Q@research.ptt.nl>; Fri, 29 May 1992 19:21 +0100 Received: by gefjon.dnl (4.1/SMI-4.1) id AA03306; Fri, 29 May 92 19:20:23 +0200 Date: Fri, 29 May 92 19:20:22 MET DST From: J.M.Kloosterman@research.ptt.nl (Hans Kloosterman) Subject: Lower-bound Kociemba's algorithm To: cube-lovers@life.ai.mit.edu Message-Id: <9205291720.AA03306@gefjon.dnl> X-Envelope-To: cube-lovers@life.ai.mit.edu X-Mailer: ELM [version 2.3 PL11] Dik Winter writes: > Using this result and the result by Hans Kloosterman the diameter of the > cube group is at most 37. I conjecture the maximal path length in phase 2 > of Kociemba's algorithm is 16, although the requirements on computer time > cq. memory do inhibit calculations at this moment (only in memory would be > feasible, but that requires 500 to 1000 MByte and computation time would be > about one day). This figure of 16 would reduce the upperbound of the groups > diameter to 28. Unfortunately Dik's conjecture for phase 2 is too optimistic. Recall the maximum distances of the 4 stages of my algorithm: 1. 7 moves within the group 2. 10 moves within the group 3. 8 moves within the group 4. 18 moves within the group (Stage 3 and 4 together requires at most 25 moves.) These number of moves are minimal and cannot be improved within their group of moves. (Stage 2 can also not be improved using all moves.)