Isomorphisms of the De Bruijn digraph and free-space optical networksReport as inadecuate




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* Corresponding author 1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués

Abstract : The de Bruijn digraph Bd, D has degree d, diameter D, dD vertices, and dD+1 arcs. It is usually defined by words of size D on an alphabet of cardinality d, through a cyclic left-shift permutation on the words, after which the rightmost symbol is changed. In this paper, we show that any digraph defined on words of a given size, through an arbitrary permutation on the alphabet and an arbitrary permutation on the word indices, is isomorphic to the de Bruijn digraph, provided that this latter permutation is cyclic. We use this result to improve from OdD+1 to the number of lenses required for the implementation of Bd, D by the Optical Transpose Interconnection System proposed by Marsden et al. Opt Lett 18 1993, 1083-1085.





Author: David Coudert - Afonso Ferreira - Stéphane Pérennes -

Source: https://hal.archives-ouvertes.fr/



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