Computer system and method using a kautz-like digraph to interconnect computer nodes and having control back channel between nodes

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)kn−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.

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)kn−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.

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)kn−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:
• VG→I×VT
• wherein VG is a set of vertices associated with the Kautz topology;
• wherein VT represents a set of vertices of a tile;
• wherein I is an index set;
• and
• wherein the tile includes multiple computer nodes.

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)kn−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.

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)kn−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.