Minimal diameter double‐loop networks: Dense optimal families

This article deals with the problem of minimizing the transmission delay in Illiac‐type interconnection networks for parallel or distributed architectures or in local area networks. A double‐loop network (also known as circulant) G(n,h) , consists of a loop of n vertices where each vertex i is also joined by chords to the vertices i ± h mod n . An integer n , a hop h , and a network G(n,h) are called optimal if the diameter of G(n,h) is equal to the lower bound k when n ∈ R [ k ] = {2 k 2 − 2 k + 2, …,2 k 2 + 2 k + 1}. We determine new dense families of values of n that are optimal and such that the computation of the optimal hop is easy. These families cover almost all the elements of R [ k ] if k or k + 1 is prime and cover 92% of all values of n up to 10 6 .