[Beowulf] torus versus (fat) tree topologies

[Don Holmgren]

On Fri, 12 Nov 2004, Patrick Geoffray wrote:

> Hi Håkon,
>
> Håkon Bugge wrote:
> > deployment times and more complicated node replacement. In larger
> > systems though, cabling of centralized switched tends to require very
> > _long_ cables, something you do not need using tori topologies.
>
> How do you close your Torus without long cables ? Unless you stack your
> nodes in a circle, you will need long cables.
>
> Patrick


Hi Patrick -

Interleave the cables.  Suppose you have 10 nodes.  The first way people
think about cabling a torus of 10 nodes is:


   1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- 10
   |                                            |
   ----------------------------------------------


In this configuration, yes, there's a long cable from 1 to 10 to close
the loop.  The shorthand way of writing this is:

    1-2-3-4-5-6-7-8-9-10-1

Instead, interleave the cables connecting every other node:

    1-3-5-7-9-10-8-6-4-2-1

The longest cable in this scheme is twice the distance between each
adjacent pair of nodes.

Don