Diameters of Weighted Double Loop Networks

Abstract Let n, h1 and h2 be positive integers such that h1, h2 i → w 1 i + h 1 ( mod n), i → w 2 i + h 2 ( mod n) for i ϵ Z nZ .Suppose that n, h1 and h2 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.