Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!sun-barr!decwrl!hplabs!hp-sdd!ncr-sd!ncrcae!hubcap!kbreinho%ug
From: kbreinho%ug@cs.utah.edu (Keith Breinholt)
Newsgroups: comp.parallel
Subject: Re: scalability of n-cubes, meshes (was: IPSC Communications)
Summary: 3D meshes will not "cook themselves" and can be made in a 2D plane.
Keywords: Ncube, scalability, 3D mesh
Message-ID: <7341@hubcap.clemson.edu>
Date: 6 Dec 89 00:31:38 GMT
Sender: fpst@hubcap.clemson.edu
Lines: 27
Approved: parallel@hubcap.clemson.edu

>}>One problem with 3D mesh is that as the processors work the heat is
>}>generated(*). >}>Thus the best you can hope for in our physics is 2D mesh.
>}> lots editted out -- Moderator

> I did not intend to claim that 3D mesh cannot be simulated in 2D per se (as a
>matter of fact it can be simulated in 1D - Turing machine). But if you notice,
>the diameter (max distance between nodes) of, say, yours (or any other) 2D
>representation of 3D mesh is going to be assymptotically much larger than the
>actual 3D mesh diameter (for the same number of nodes). So, in fact your
>suggestion can be read as "pretend you have 3D, but implement it in 2D in
>reality", and this does not contradict anything I have said.

I think you misunderstood me, partly due to the wording of my reply.  What I was
trying to say is that a 3D mesh CAN be reproduced on a 2D plane,
not simulated or pretended in 2D.

A hexagon has 6 sides.  A cube has 6 sides.  If I can produce 6 sets of connections
to neighboring processors in a 2D plane I have effectively produced a 3D connection
scheme in a 2D plane.  And as stated before, this type of representation requires no
more cooling than existing planar boards.  Which does contradict your statement.

If 3D meshes "cook themselves" it will be due to a design flaw, not because physics
dictates it so.

Keith L. Breinholt             kbreinho@ug.utah.edu or usiklb@vm.usi.utah.edu
Utah Supercomputing Institute
(801) 581-4439