Optimal Designs of Directed Double-Loop Networks.

Let n, s be positive integers such that . A directed double-loop network G(n ; 1, s) is a directed graph (V, E), where V = Zn = {0, 1, 2, ... , n-1 }, E = { i, =0, 1, 2, ... , n-1 }. An attention deserving problem is: for a given positive integer n, how to choose an integer s such that the diameter of G(n; 1, s) is minimal. An algorithm, where O(k) is upper-bounded by O(n0.25), is given in this paper to determine s such that the diameter of G(n; 1, s) is minimal. Keywords: directed double-loop networks, diameter, optimal design, k-tight optimal. [ABSTRACT FROM AUTHOR]