Date: 28 June 1984 00:17-EDT From: Alan Bawden Subject: The Cube meets Massive Parallelism To: CUBE-LOVERS @ MIT-MC cc: CM-I @ MIT-MC In-reply-to: Msg of Tue 26 Jun 84 10:20 EDT from Bernard S. Greenberg Since I spend most of my time these days thinking about designing and programming massively parallel computers, it occured to me to think about applying such machines to exploring the Cube's Group. Here are some preliminary thoughts. When we say "massively parallel" we are talking at least a quarter million simple processors. This is enough processors to give all of the positions 5 or fewer quarter twists away from home their own processor. A million processors would be enough to get up to 6 Qs, but lets not push our luck. Given a machine like the MIT Connection Machine we could set up a database in which every processor representing a configuration knew the addresses ot the 12 other processors representing its 12 closest neighbors, in almost no time at all. (Processors 5 Qs away from home would have null pointers for their unrepresented 6 Q neighbors.) A conservative statement would be that operations like generating a list of all identities of length 10 or less (which has previously taken us hours to accomplish) could be done so fast that the machine could generate output faster than you could read it. Since this is all so absurdly easy, there must be ways to go beyond this to generate significant new results using this (promised) new kind of hardware. Perhaps Dave Christman, who is both a cube hacker, and a designer of algorithms for massively parallel machines, could be persuaded to devote some spare cycles to figuring out ways to brute-force the Cube using such a machine.