Sparse asymmetric connectors in communication networks

R. Ahlswede, H. Aydinian
2005 Electronic Notes in Discrete Mathematics  
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 ≤ N 1/2−ε , ε > 0. However, the known
more » ... xplicit constructions with n ≤ √ Here we present a simple combinatorial construction for (n, N, 2)-connectors of size O(N log 2 n). We also consider depth 2 faulttolerant connectors under arc or node failures.
doi:10.1016/j.endm.2005.07.004 fatcat:ll7z2he47ngzrnys3seeuky65i