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-epsilon-R[k] = {2k2 - 2k + 2,...,2k2 + 2k + 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).