# Digraph Isomorphisms and Free Space Optical Networks

1 SLOOP - Simulation, Object Oriented Languages and Parallelism
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - 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)\$.\\
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https://hal.inria.fr/inria-00072841
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:04:45 AM
Last modification on : Saturday, May 8, 2021 - 2:02:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:24:49 PM

### Identifiers

• 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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