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Minimal diameter double‐loop networks: Dense optimal families
Author(s) -
Bermond J.C.,
Tzvieli Dvora
Publication year - 1991
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230210102
Subject(s) - circulant matrix , combinatorics , mathematics , loop (graph theory) , vertex (graph theory) , cover (algebra) , upper and lower bounds , interconnection , hop (telecommunications) , vertex cover , discrete mathematics , graph , computer science , telecommunications , mechanical engineering , mathematical analysis , engineering
Abstract 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 .