# On Arbitrary Waksman Networks and their Vulnerability

1 SLOOP - Simulation, Object Oriented Languages and Parallelism
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Motivated by problems in telecommunication satellites, we investigate rearrangeable permutation networks made of binary switches. A simple counting argument shows that the number of switches necessary to build a $n \times n$ rearrangeable network (i.e. capable of realizing all one-to-one mappings of its $n$ inputs to its $n$ outputs) is at least $\psln! = n\log_2{n} - n\log_2{e} + o(n)$ as $n\rightarrow\infty$. For $n = 2^r$, the $r$-dimension- al Bene\vs network gives a solution using $n\log_2{n} - \frac{n}{2}$ switches. Waksman, and independently Goldstein and Leibholz, improved these networks using $n\log_2{n}-n+1$ switches. We provide an extension of this result to arbitrary values of~$n$, using $\slog{i}{n}$ switches. The routing algorithm used in Bene\v{s} networks is also generalized for arbitrary values of~$n$. Finally the fault-tolerance issue of these networks is discussed.
Keywords :
Type de document :
Rapport
RR-3788, INRIA. 1999
Domaine :

https://hal.inria.fr/inria-00072871
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 11:08:46
Dernière modification le : mercredi 31 janvier 2018 - 10:24:04
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:25:48

### Identifiants

• HAL Id : inria-00072871, version 1

### Citation

Bruno Beauquier, Eric Darrot. On Arbitrary Waksman Networks and their Vulnerability. RR-3788, INRIA. 1999. 〈inria-00072871〉

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