From dik@cwi.nl Wed May 20 17:14:12 1992 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) id AA00649; Wed, 20 May 92 17:14:12 EDT Received: from boring.cwi.nl by charon.cwi.nl with SMTP id AA10861 (5.65b/2.10/CWI-Amsterdam); Wed, 20 May 1992 23:13:12 +0200 Received: by boring.cwi.nl id AA02174 (5.65b/2.10/CWI-Amsterdam); Wed, 20 May 1992 23:13:11 +0200 Date: Wed, 20 May 1992 23:13:11 +0200 From: Dik.Winter@cwi.nl Message-Id: <9205202113.AA02174.dik@boring.cwi.nl> To: cube-lovers@ai.mit.edu, reid@math.berkeley.edu Subject: Re: assorted results > > Currently I am calculating the > > maximal distance in stage 1. It will take a bit of time because I have to > > consider 2,217,093,120 possibilities. But I think that the method I have > > is feasible. > how much time do you anticipate the job will take? A few days. I started yesterday night at 2:30 AM, it is now 11:05 PM. I have calculated the distances for approximately 145 million configurations. The majority of the work has been done sinc 6:00 PM. (I am using 39 SGI Indigo's, 1 Large SGI, 2 processors of an SGI file server and the scalar (SPARC) processor of an FPS, so it is lots of computer time!) > it seems that we'd > get a much better improvement (of kloosterman's bound) by calculating > the maximal distance in stage 2. of course, this requires going through > 19,508,428,800 possibilities (nearly 9 times as many). is this feasible? Right. But is not feasible, at least I do not see possibilities at this moment. My estimate is that it would take much more than 9 times as much. The reason is that the algorithm as I have organized it allows a lot of shortcuts. What I do is in the space of order 2048 * 2187 * 495 assign to each processor in turn a slice of the 2048 dimension. Within that slice, going from 0 moves until every configuration has been assigned a distance, a path is searched for the given distance. The major shortcut comes when a path is found. Using configurations with known distance, U, D, L and R turns are applied and also F2 and L2 turns to calculate new distances. For those moves the flip does not change. This makes that I have to search paths for only about 10% of the cases. I see no way (yet) to do similar things for phase 2. dik