Independent connections: an easy characterization of baseline-equivalent multistage interconnection networks

AbstractIn this paper we study topological properties of multistage interconnection networks. We define the interconnection scheme between two stages as a pair of functions (f, g) which associate with a cell or node x, labelled as a binary string, his two sons f(x) and g(x). We consider a class of connections called independent connections. Using our graph characterization of networks topologically equivalent to the Baseline network, we show that all the Banyan networks built with independent connections are isomorphic. Finally, we show that if the interconnection scheme is defined by using permutations on the links induced by a permutation of the index digit (PIPID permutation) then the connection is independent. As these PIPID are associated with a very simple bit directed routing, they are used to define most of the networks introduced in the literature. Therefore all these networks are easily shown to be equivalent