Method for interconnecting and system of interconnected processing elements by controlling network density

Claim 2

A computer system in a form of a non-binary hypercube comprising: a plurality of nodes, N, where N=b n , b and n being positive integers and b>2, each node having an identifying address numbered according to a number system base b; means for determining an address of each of said plurality of nodes; and means for interconnecting each respective node of said plurality of nodes to nodes having addresses differing from the respective node's address by exactly one digit to form a toroidal network, a number of connections per node being μlog b N, where μ=2d, 1≦d≦b/2 if b is even and 1≦d≦(b-1)2 if b is odd, except if b is even and d=b/2, in which case μ=b-1, to thereby control density of said toroidal network, wherein two nodes, x and y, of the network are connected if and only if 1. an address of x differs from an address of y in exactly one digit, and 2. for a digit i where x i ≠y i , y i =(x i +j) mod y or y i =(x i +j) mod y for some j≦d.

Claim 3

The computer system recited in claim 1 wherein b=8, n-1, and d=2.

Claim 4

The computer system recited in claim 1 wherein b=8, n=1, and d=3.

Claim 5

The computer system recited in claim 1 wherein b=8, n=1, and d=4.

Claim 6

The computer system recited in claim 1 wherein b=5, n=3, and d=1.

Claim 7

The computer system recited in claim 1 wherein b=8, n=4, and d=1.

Claim 8

A computer implemented method of interconnecting a plurality of nodes in a network comprising steps of: providing a plurality of nodes; defining b and n such that a number N of said plurality of nodes equals b n and b and n are positive integers and b>2; choosing a positive integer d such that 1≦d≦b/2 if b is even and 1≦d≦(b-1)/2 if b is odd; defining an address for respective ones of each of the plurality of nodes by numbering them using numbers represented by a base b numbering system; determining an address of each of said plurality of nodes; and connecting two nodes of said plurality of nodes, to thereby form a toroidal network, if and only if an address of a first one of said two nodes of said plurality of nodes differs from an address of a second one of said two nodes of said plurality of nodes in exactly one digit, a i th digit and, for a unique i th digit of the addresses of said two nodes, symbolized by x i and y i , respectively, where x i ≠y i , y i =(x i +j) mod y or y i =(x i +j) mod y for some j≦d to thereby control density of said toroidal network.

Claim 9

A computer implemented method of interconnecting a plurality of nodes in a network comprising steps of: providing a plurality of nodes; defining b and n such that a number N of said plurality of nodes equals b n and b and n are positive integers and b>2; choosing a positive integer d such that 1≦d≦b/2 if b is even and 1≦d≦(b-1)/2 if b is odd; defining an address for respective ones of each of the plurality of nodes by numbering them using numbers represented by a base b numbering system; determining an address of each of said plurality of nodes; and connecting two nodes of said plurality of nodes, to thereby form a toroidal network, if and only if an address of a first one of said two nodes of said plurality of nodes differs from an address of a second one of said two nodes of said plurality of nodes in exactly one digit, a i th digit and, for a unique i th digit of the addresses of said two nodes, symbolized by x i and y i , respectively, where x i ≠y i , y i =(x i +j) mod y or y i =(x i +j) mod y for some j≦d to thereby control density of said toroidal network.