Sparse Asymmetric Connectors in Communication Networks

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 ≤ N1/2−ε, ε > 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 fault– tolerant connectors under arc or node failures.