[Beowulf] Network considerations for new generation cheap beowulfcluster

Peter St. John peter.st.john at gmail.com
Tue May 22 09:19:54 PDT 2007

A hypercube (http://en.wikipedia.org/wiki/Hypercube) also gets you
exponential space; the max hops is the dimension (3 for a 3-dimensional
cube) and the number of nodes is exp(base 2) of the dimension (8 vertices on
a cube). To do a tesseract (4-cube), which looks like two cubes nested,
you'd need 4 ports per node, 16 nodes, 32 cables, max hop 4. I've poked
around and don't see a great 4 ports per node solution; I like the
suggestion of putting a router on a motherboard.

But you've made me curious about this Kautz and de Bruijn graphs, I'll go
look, thanks.

On 5/22/07, Larry Stewart <larry.stewart at sicortex.com> wrote:
> Robert G. Brown wrote:
> > On Tue, 22 May 2007, Larry Stewart wrote:
> >
> >> What would the advantages of a diamond lattice be?  In terms of
> >> bisection and diameter?
> >> Ease of wiring?
> >
> >
> > Four ports per system, probably, in a 3d lattice.  3d is good because
> > the volume (number of hosts) scales like the maximum number of hops
> > between hosts cubed.
> Ah.  I see that.  I looked at the diamond lattice picture in
> http://phycomp.technion.ac.il/~nika/diamond_structure.html
> and it did make my head twinge.
> With Kautz or deBruijn graphs, you get an exponential number of nodes,
> for node degree
> k >= 2, and diameter (hopcount D) you get O(k**D) nodes.  However, you
> don't get any
> obvious mapping of 2D or 3D problems to the graph.   You could do this
> with two
> NICs per node, if you can send the transmit data and the receive data to
> different places.
> Of course even on BlueGene/L they use simulated annealing to map the
> problem to the
> machine, because the obvious mapping is often not the best one.
> See "Optimizing Task Layout on the BlueGene/L Supercomputer" in IBM JSRD
> March 2005.
> -Larry
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