Construction of asymmetric connectors of depth two

Authors:
R. Ahlswede;H. Aydinian
Affiliations:
Department of Mathematics, University of Bielefeld, Bielefeld, Germany;Department of Mathematics, University of Bielefeld, Bielefeld, Germany
Venue:
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Year:
2006

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Abstract

An (n, N)-connector of depth d 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 at most d joining each input to its corresponding output. In this paper we consider the problem of construction of sparse depth two connectors with n ≪ N. We use posers of star products and their matching properties to construct such connectors. In particular, this gives a simple explicit construction for connectors of size O(N log n/log log n). Thus our earlier idea to use other posets than the family of subsets of a finite set was successful.