Abstract
An (n,N,d )–connector is an acyclic digraph with n inputs and N outputs in which for any injective mapping of input vertices into output vertices there exist n vertex disjoint paths of length d joining each input to its corresponding output. We consider the problem of construction of sparse (n,N,2)–connectors (depth 2 connectors) when n≪N. The probabilistic argument in [1] shows the existence of (n,N,2)–connectors of size (number of edges) O(N) if \(n\leq N^{1/2-\varepsilon},\ \varepsilon >0\). However, the known explicit constructions with \(n\leq\sqrt{N}\) in [6],[1],[2] are of size O\((N\sqrt{n})\). Here we present a simple combinatorial construction for (n,N,2)–connectors of size O(N log2 n). We also consider depth 2 fault–tolerant connectors under arc or node failures.
Supported by DFG-Schwerpunkt Nr.1126 “Algorithmik großer und komplexer Netzwerke”.
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© 2006 Springer-Verlag Berlin Heidelberg
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Ahlswede, R., Aydinian, H. (2006). Sparse Asymmetric Connectors in Communication Networks. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_66
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DOI: https://doi.org/10.1007/11889342_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
Online ISBN: 978-3-540-46245-3
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