Computer system and method using a kautz-like digraph to interconnect computer nodes and having control back channel between nodes
Computer system and method using a Kautz-like digraph to interconnect computer nodes and having control back channel between nodes. 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 data 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 each x,y pair includes a unidirectional control link from node y to node x to convey flow control and error information from a receiving node y to a transmitting node x.
1. A 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 data interconnections from a computer node x to a computer node y in the Kautz topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k;
wherein each x,y pair includes a unidirectional control link from computer node y to computer node x to convey flow control and error information from a receiving computer node y to a transmitting computer node x; and
wherein j represents a corresponding node in the multi-node computer system.
2. The multi-node computer system of claim 1 wherein a receiving computer node y transmits control packets on a control link to transmitting computer node x to identify a last correctly received data packet from the transmitting computer node, and to identify whether an error has been detected during transmission of the received data packet.
3. The multi-node computer system of claim 2 wherein a transmitting computer node x stores transmitted packets and keeps the transmitted packets available for replay in response to control messages on the control link.
4. The multi-node computer system of claim 1 wherein a receiving computer node y transmits buffer status information to a transmitting computer node x to identify buffer availability of downstream computer nodes.
5. The multi-node computer system of claim 4 wherein a transmitting computer node x includes logic to transmit a packet downstream only if all necessary buffers are available.
6. A 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 data interconnections from a computer node x to a computer node y in the Kautz topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k;
wherein each x,y pair includes a unidirectional control link from computer node y to computer node x to convey flow control and error information from a receiving computer node y to a transmitting computer node x; and
wherein j is an integer value.
7. A 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 data interconnections from a computer node x to a computer node y in the Kautz topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k;
wherein each x,y pair includes a unidirectional control link from computer node y to computer node x to convey flow control and error information from a receiving computer node v to a transmitting computer node x; and
wherein the plurality of computer nodes in the Kautz topology are numbered from zero to O-1.
8. A 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 data interconnections from a computer node x to a computer node y in the Kautz topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k;
wherein each x,y pair includes a unidirectional control link from computer node y to computer node x to convey flow control and error information from a receiving computer node y to a transmitting computer node x;
wherein the Kautz topology is uniformly tiled based on one-to-one mapping in accordance with equation:
V G →I×V T
wherein V G is a set of vertices associated with the Kautz topology;
wherein V T represents a set of vertices of a tile;
wherein I is an index set; and
wherein the tile includes multiple computer nodes.
9. The multi-node computer system of 8 , wherein a given x,y pair is an edge within a tile and t −1 (i,x), t −1 (i,y) is an edge of the Kautz topology.
10. A 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 data interconnections from a computer node x to a computer node y in the Kautz topology satisfies a relationship y=(−x*k−j) mod O, where 1≦j≦k;
wherein each x,y pair includes a unidirectional control link from computer node y to computer node x to convey flow control and error information from a receiving computer node y to a transmitting computer node x; and
wherein the Kautz topology is defined by the relationship y=(−x*k−j) mod O, where 1≦j≦k; wherein j is an integer.
11. A method for defining a multi-node computer environment, the method comprising:
creating a computer system to include 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 data interconnections from a computer node x to a computer node y in the Kautz topology to satisfy relationship y=(−x*k−j) mod O, where 1≦j≦k; and
providing each x,y pair to include a unidirectional control link from computer node y to computer node x, the unidirectional control I ink conveying flow control and error information from a receiving computer node y to a transmitting computer node x; and
wherein j is an integer value.
12. The method of claim 11 , wherein j represents a corresponding node in the multi-node computer system.
13. The method of claim 11 , wherein the plurality of computer nodes in the Kautz topology are numbered from zero to O-1.
14. The method of claim 11 , wherein the Kautz topology is uniformly tiled based on one-to-one mapping in accordance with equation:
V G →I×V T
wherein V G is a set of vertices associated with the Kautz topology;
wherein V T represents a set of vertices of a tile;
wherein I is an index set; and
wherein the tile includes multiple computer nodes.
15. The method of claim 14 , wherein a given x,y pair is an edge within a tile and t −1 (i,x), t −1 (i,y) is an edge of the Kautz topology.
16. The method of claim 11 , wherein the Kautz topology is defined by the relationship y=(−x*k−j) mod O, where 1≦j≦k; wherein j is an integer.