Diameters of weighted double loop networks.

Let n, h sub 1 and h sub 2 be positive integers such that h sub 1, h sub 2 n and w sub 1, w sub 2 be positive real numbers. We define the weighted double loop network G(n, h sub 1, h sub 2; w sub 1, w sub 2) as the directed graph with vertex set Z/nZ = {0,1,....,n - 1} and weighted edges i going to i + h sub 1 (mode n) under w 1, i going to i + h sub 2 (mod n) under w 2, for i belongs to Z/nZ. Suppose than n, h sub 1 and h sub 2 are relatively prime. The weight of a directed path is the sum of weights on the edges. The distance d(x,y) between two vertices x and y is defined as the minimum weight of directed paths from x to y. The weighted diameter of this network, is defined as the maximum d(x,y) among all x and y. In this paper, we obtain an O(log n) algorithm for computing the diameter.