Archives

- Beowulf
- Beowulf Announce
- Scyld-users
- Beowulf on Debian

# [Beowulf] Network considerations for new generation cheap beowulfcluster

Many of your questions may have already been answered in earlier discussions or in the FAQ. The search results page will indicate current discussions as well as past list serves, articles, and papers.

Search

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.
Peter

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
>
> _______________________________________________
> Beowulf mailing list, Beowulf at beowulf.org
> To change your subscription (digest mode or unsubscribe) visit
> http://www.beowulf.org/mailman/listinfo/beowulf
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www.scyld.com/pipermail/beowulf/attachments/20070522/f061303c/attachment.html
```