Computer system and method using efficient module and backplane tiling to interconnect computer nodes via a Kautz-like digraph

A multinode computing system, comprising:

• a large plurality of computing nodes interconnected via a Kautz topology having order O, diameter n, and degree k;
• wherein the order=(k+1)kn−1;
• wherein the interconnections from a node x to a node y in the topology satisfies the relationship y=(−x*k−j) mod O, where 1≦j≦k;
• and
• wherein the computing nodes are arranged onto a plurality of modules;
• wherein each module has km nodes, and each node on the module can be assigned a label d1 . . . dmεZkm such that inter-node connections that are intra-module correspond to a subset of the edges (d1 . . . dm, d2 . . . dm+1) of a de Bruijn graph of diameter m and degree k, subject to the condition that there are no directed closed loops formed from the inter-node connections on a module.

A multinode computing system, comprising:

• a large plurality of computing nodes interconnected via a de Bruijn topology having order O, diameter n, and degree k;
• wherein the order O=kn;
• wherein the interconnections from a node x to a node y in the topology satisfies the relationship y=(x*k+j) mod O, where 0≦j≦k−1;
• and
• wherein the computing nodes are arranged onto a plurality of modules each module having an equal plurality of computing nodes thereon.