From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 20:47:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA10386 for ; Wed, 10 Mar 1999 20:47:01 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 4 Mar 1999 23:09:00 -0500 From: michael reid Message-Id: <199903050409.XAA24597@cauchy.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Edges only, Ignoring Flips, Face Turn Metric jerry writes > I have completed a God's Algorithm run in the face turn metric for the > group consisting of edges only ignoring flips. The size of the group is > therefore 12! The results are as follows: [ ... ] very interesting. i hope that you'll also do the quarter turn metric. > I have come to believe that any corners only (with or without twist) or > edges only (with or without flip) group, or the group which keeps both > corners and edges but without twists and flips, will be a fairly poor > pattern data base for IDA*. The problem is that any such search space > will have a diameter which is too small, and more importantly will have an > average distance from Start which is too small. another shortcoming of this coset space for ida* is that transformations aren't easy to compute. for the cosets spaces i've used, they always split up as a product of smaller coset spaces. then i use transformation tables for everything. ida* spend a lot of time moving from a position to its neighbors. instead of keeping the cube position, i just keep track of which coset i'm in. then i need to find out what coset i'll be in if i apply the turn F (for example). i always do this by using transformation tables. to simplify things, suppose that my coset space had 1000000 cosets. i could use a table with 18 * 1000000 entries that tells me which coset i go to by applying a given turn. if my coset space is a product of two spaces, each with 1000 cosets, then i only need a tranformation table with 18 * 1000 entries for the first coordinate and one of the same size for the second coordinate. this is really addressing implementation issues of ida*, not so much the effectiveness of it. mike