# Digraph Isomorphisms and Free Space Optical Networks

1 SLOOP - Simulation, Object Oriented Languages and Parallelism
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : The de Bruijn digraph B(d,D) 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 and alphabets of the same size, through an arbitrary permutation on the alphabet and an arbitrary permutation on the word indices, is isomorphic to the de Bruijn, provided that this latter permutation is cyclic. As an application, we recall that it is known that the Optical Transpose Interconnection System from UCSD can implement the de Bruijn interconnections for n$nodes, for a fixed d, with O(n) lenses. We show here how to improve this hardware requirement to$\Theta(\sqrtn)\$.\\
Keywords :
Type de document :
Rapport
[Research Report] RR-3817, INRIA. 1999
Domaine :

https://hal.inria.fr/inria-00072841
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 11:04:45
Dernière modification le : lundi 23 avril 2018 - 10:52:05
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:24:49

### Identifiants

• HAL Id : inria-00072841, version 1

### Citation

David Coudert, Afonso Ferreira, Stéphane Pérennes. Digraph Isomorphisms and Free Space Optical Networks. [Research Report] RR-3817, INRIA. 1999. 〈inria-00072841〉

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