Patent ID: 7453813

Claim:
A method for constructing a two level private network-to-network interface (PNNI) network, the PNNI network comprising a plurality of nodes N, comprising dividing the nodes into a number of nodes x* 1 interconnected in each level one peer group and a number x* 2 of level one peer groups, and interconnecting the level one peer groups, wherein the number of nodes x* 1 interconnected in each level one peer group is determined using the following steps: (1) Set s =( s 1 , s 2 ) such that e s 1 e s 2 =N, and set t such that e s 1 +γ 0 e (γ s 1 + s 2 ) =e t , (2) set f 2 ( s , t )=e α t +κ 0 e (α s 1 +κ s 2 ) , set ε 1 =e α t /f 2 ( s , t ) and ε 2 =κ 0 e (α s 1 +κ s 2 ) /f 2 ( s , t ), (3) define δ=(δ 1 , δ 2 , δ 3 , δ 4 ) by δ 1 = 1 , δ 2 = ε 1 ⁢ α ⁡ ( 1 - γ ) + ε 2 ⁡ ( κ - α ) 2 - γ , δ 3 = ε 1 ⁢ α - δ 2 , ⁢ δ 4 = ε 1 ⁢ α + ε 2 ⁢ κ - δ 2 , (4) set b 1 =log(N), b 2 =log (δ 2 /(δ 1 α)), b 3 =log (δ 3 /(γ 0 ε 1 α)), define (s, t)=(s 1 , s 2 , t) by s 1 =( b 1 +b 2 −b 3 )/(2−γ), s 2 =b 1 −s i , t=s 1 −b 2 , and set d=(s, t)−( s , t ), (5) set θ* to the point minimizing f 2 (( s , t )+θd) over the range 0≦θ≦1, and set ( s , t )←( s , t )+θ*d, (6) set x 1 *=e s 1 and x 2 *=e s 2 where S 1 represents the log of the number of nodes in each level one peer group, S 2 represents the log of the level one peer groups, e is the numerical constant, N is the total given number of nodes in the network, α represents the time complexity of computing a minimum cost path in a flat network, γ and γ 0 are constants characterizing the number of border nodes of each level one peer group, κ and κ 0 characterize the number of lower level peer groups in each higher level peer group that is visited by a network connection, and f 2 , ε 1 , ε 2 ,t, t , d, b 1 , b 2 ,b 3 , and Θ are temporary variables.