Computer system and method using efficient module and backplane tiling to interconnect computer nodes via a Kautz-like digraph
Computer systems and methods using efficient module and backplane tiling to interconnect computer nodes via a Kautz-like digraph. A multinode computing system includes a large plurality of computing nodes interconnected via a Kautz topology having order O, diameter n, and degree k. The order equals (k+1)k n−1 . The interconnections from a node x to a node y in the topology satisfy the relationship y=(−x*k−j) mod O, where 1≦j≦k, and the computing nodes are arranged onto a plurality of modules. Each module has an equal plurality of computing nodes on it. A majority of the inter-node connections are contained on the plurality of modules and a minority of the inter-node connections are inter-module connections. Inter-module connections are routed among modules in parallel on an inter-module connection plane.
1. A scalable, multi-node computer system for providing efficient transmission of data amongst interconnected modules, the multi-node computer system comprising:
a plurality of computer nodes interconnected via a Kautz topology having order O, diameter n, and degree k;
wherein the order O=(k+1)k n−1 ;
wherein interconnections from a computer node x to a computer node y in the topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k; and
wherein the computer nodes are arranged onto a plurality of modules, each module of the plurality of modules having an equal number of computer nodes thereon.
2. The multi-node computer system of claim 1 , wherein a majority of the inter-node connections are contained on the plurality of modules and a minority of the inter-node connections are inter-module connections.
3. The multi-node computer system of claim 1 , wherein the amount of inter-node connections contained on the plurality of modules is optimal.
4. The multi-node computer system of claim 1 , wherein a subset of the inter-node connections are inter-module connections and the subset routes data among modules on an inter-module connection plane.
5. A scalable, multi-node computer system for providing efficient transmission of data amongst interconnected modules, the multi-node computer system comprising:
a plurality of computer nodes interconnected via a Kautz topology having order O, diameter n, and degree k;
wherein the order O=(k+1)k n−1 ;
wherein interconnections from a computer node x to a computer node y in the Kautz topology satisfy a relationship y=(−x*k−j) mod O, where 1≦j≦k; and
wherein the plurality of computer nodes are arranged onto a plurality of modules;
wherein each module has k m nodes, and each node on the module is assigned a label d 1 . . . d m εZ k m such that inter-node connections that are intra-module correspond to a subset of the edges (d 1 . . . d m , d 2 . . . d m + 1 ) of a de Bruijn graph of diameter m and degree k, subject to a condition that there are no directed closed loops formed from the inter-node connections on a module.
6. The system of claim 5 , wherein a number of intra-module connections is optimal.
7. The system of claim 5 , wherein the d 1 's are expressed as a function of the node labels S 0 . . . S n of the Kautz graph through
d i =f ( c i +n−m,c i )
wherein f(x,y) is a function which for fixed X acts a permutation on Z k through y→f(X,y) and which for fixed Y acts as a permutation on Z k through x→f (x,Y) and where c i 's encode the Kautz coordinates S i through c i =S i −S i−1 −1 mod(k+1).
8. The system of claim 7 , wherein f(x,y) equals x+y mod k.
9. The system of claim 7 , wherein f(x,y) equals x−y mod k.
10. The system of claim 5 , wherein each module is degree 3 and contains 27 computing nodes.
11. The system of claim 5 , wherein a subset of the inter-node connections are inter-module connections and the subset routes data among modules on an inter-module connection plane.