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De Bruijn isomorphisms and free space optical networks

David Coudert 1 Afonso Ferreira 1 Stéphane Pérennes 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
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. This work is motivated by the next application. 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 Θ(√n)
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David Coudert, Afonso Ferreira, Stéphane Pérennes. De Bruijn isomorphisms and free space optical networks. 14th International Parallel and Distributed Processing Symposium (IPDPS 2000), May 2000, Cancun, Mexico. pp.769 - 774, ⟨10.1109/IPDPS.2000.846063⟩. ⟨inria-00429190⟩

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