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From: wilson@carcoar.Stanford.EDU (Paul Wilson)
Newsgroups: comp.parallel
Subject: scalability of n-cubes, meshes (was: IPSC Communications)
Summary: meshes most scalable?
Keywords: iPSC Parallel hypercubes meshes torus scalability
Message-ID: <7178@hubcap.clemson.edu>
Date: 22 Nov 89 21:31:51 GMT
Sender: fpst@hubcap.clemson.edu
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Approved: parallel@hubcap.clemson.edu

My admittedly naive intuitions would say that only meshes are truly
scalable, since you have to pack things into real (<= 3D) space.
Hypercubes end up needing long wires to project a higher-dimensional
graph into 2- or 3-space.  As processor speeds increase (and the
speed of light presumably doesn't) these end up being slower
than other links and destroy the scalability of n-cubes.

It would *seem* to me that a 3D mesh is the only way to go
because that's the highest dimensionality you can embed into
a 3D reality.  You get constant time per hop, no problem.

Now could somebody summarize Dally's argument that 2D meshes
(and toruses) are better?  I can see why you can wrap a 2D mesh
around to make a torus one way, but can't you get much
better packing by using a 3D mesh with its higher connectivity?
It will have edges rather than wrapping around transparently,
but that's the only way to avoid long wires in the limit.

Any comments?  I'm also curious about the pros and cons of
CM-style combinations of mesh and n-cube routing systems.

thanks prematurely,

   Paul


Paul R. Wilson                         
Software Systems Laboratory               lab ph.: (312) 996-9216
U. of Illin. at C. EECS Dept. (M/C 154)   wilson@carcoar.stanford.edu
Box 4348   Chicago,IL 60680