• Constructions of sparse asymme...

Result: Constructions of sparse asymmetric connectors with number theoretic methods

Title:
Constructions of sparse asymmetric connectors with number theoretic methods
Authors:
BALTZ, Andreas, JÄGER, Gerold, SRIVASTAV, Anand
Source:
Networks (New York, NY). 45(3):119-124
Publisher Information:
New York, NY: John Wiley & Sons, 2005.
Publication Year:
2005
Physical Description:
print, 15 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Télécommunications, Telecommunications, Réseaux téléinformatiques. Rnis, Teleprocessing networks. Isdn, Connecteur, Connector, Conector, Méthode combinatoire, Combinatorial method, Método combinatorio, Réseau communication, Communication network, Red de comunicación, Théorie nombre, Number theory, Teoría números, Conception réseau, Réseau réarrangeable, Rearrangeable network, Somme restreinte, Sparse switch, combinatorial number theory, connector, permuter, rearrangeable network, restricted sums, sparse switch
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Mathematisches Seminar, Christian-Albrechts-Universitat zu Kiel, Christian-Albrechts-Platz 4, 24118 Kiel, Germany
ISSN:
0028-3045
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16712334
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Telecommunications and information theory
Accession Number:
edscal.16712334
Database:
PASCAL Archive

Further Information

We consider the problem of connecting a set 1 of n inputs to a set O of N outputs (n≤N) by as few edges as possible such that for every injective mapping f: I → O there are n vertex disjoint paths from i to f(i) of length k for a given k e IN. For k = Ω(log N + log2 n) Oruç (J Parallet Distributed Comput 1994, 359-366 [10]) gave the presently best (n, N)-connector with O(N+ n . log n) edges. For κ = 2 and N the square of a prime, Richards and Hwang (1985) described a construction using N[√n+5/4 - 1/2] +n [√n+5/4- 1/2]√N edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ(N) edges, if n ≤ N1 2-ε for some ∈ > 0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most N3n/4 + 2n 3n/4 N edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.