Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uunet!ncrlnk!ncrcae!hubcap!boulder!foobar!grunwald
From: boulder!foobar!grunwald@ncar.UCAR.EDU (Dirk Grunwald)
Newsgroups: comp.parallel
Subject: Re: scalability of n-cubes, meshes (was: IPSC Communications)
Message-ID: <7211@hubcap.clemson.edu>
Date: 27 Nov 89 20:39:57 GMT
Sender: fpst@hubcap.clemson.edu
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Approved: parallel@hubcap.clemson.edu

>>> On 22 Nov 89 21:31:51 GMT, wilson@carcoar.Stanford.EDU (Paul Wilson) said:
Paul> It would *seem* to me that a 3D mesh is the only way to go
Paul> because that's the highest dimensionality you can embed into
Paul> a 3D reality.  You get constant time per hop, no problem.

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

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

You can embed a torus in a plane if you allow wires to overlap. E.G.
package torus:

	    +-----------------------------+
	    |		      		  |
	    A <-> B <-> C <-> D <-> E <-> F
	 
as	 
	+-----------+ +---------+
	|           | |		|
	A <-> B     F--   C--+  E <-> D
	      |		  |  |        |
	      +-----------+  +--------+

you decrease the maximum wire length at the expense of increased
average wire length. Similar constructions are possible for 2 & 3-d
tori.

the problem is you can't extend this system as easily, i.e. adding
more processors becomes a pain. There are other possibilites because
the world is not planer. You could also package the above as:

	A B
       +++++
	D C

where +++++ is the PC board and you use bond-through connections.
Or where +++++ is a cabinet and you use wire connectors.
Last I heard, Dally is now advocating a 3-D mesh.

Of course, multi-layer PC boards make hypercubes appear better.
Consider something like the Ncube system that wires hypercubes
together using PC boards.

I think that if you use free lasers or fiber optics, you'd probably go
for hypercubes again, or a hypercube of shared memory machines.


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