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Minimal diameter double-loop networks: Dense optimal families

Jean-Claude Bermond 1 Dvora Tzvieli 2
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
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 networks (also known as circulant) G (n,h) consist 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+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 +1 is prime and cover 92% of all values of n up to 10(6).
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Submitted on : Wednesday, November 18, 2020 - 10:44:17 PM
Last modification on : Tuesday, December 7, 2021 - 4:10:50 PM
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Jean-Claude Bermond, Dvora Tzvieli. Minimal diameter double-loop networks: Dense optimal families. Networks, Wiley, 1991, 21 (1), pp.1-9. ⟨10.1002/net.3230210102⟩. ⟨hal-03013377⟩



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