Sparse asymmetric connectors in communication networks

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 0. However, the known explicit constructions with n < √N in [6],[1],[2] are of size O(N√n). Here we present a simple combinatorial construction for (n, N, 2)-connectors of size O(N log2 n). We also consider depth 2 faulttolerant connectors under arc or node failures. © Springer-Verlag Berlin Heidelberg 2006.