Minimal diameter double-loop networks: Dense optimal families

✍ Scribed by J.-C. Bermond; Dvora Tzvieli

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 370 KB
• Volume: 21
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/net.3230210102

✦ Synopsis

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 E R [ k ] = {2k2 -2k + 2 , . . . , 2k2 + 2k + I}. 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 lo6.