On the Complexity of Strictly Nonblocking Concentration Networks

Abstract

A concentration network is a contact switching network that provides a number of potential users (connected to its inputs) with access to a smaller number of equivalent resources (connected to its outputs). Its basic property is that any sufficiently small subset of the inputs can be simultaneously connected by disjoint paths to distinct outputs, although the particular outputs to which they are to be connected cannot, in general, be specified arbitrarily. We show that a strictly nonblocking concentration network must have at least <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3n \log_{3} n - O(n)</tex> contacts where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is the number of connections to be established simultaneously.