Characterizing the bit permutation networks obtained from the line digraphs of bit permutation networks

Abstract

A bit permutation network is an s-stage interconnection network composed of d(n-1) d x d crossbar switches in each stage. This class of networks includes most of the multistage interconnection networks. Recently, Chang et al, [Networks 33 (1999), 261-267] showed that an s-stage d-nary bit permutation network N with d(n) inputs (outputs) can be characterized by an (s - 1)-vector (k(1),..., k(s-1)), where k(1) is an element of {1, ..., n - 1}. In this paper, we give a simple (but not trivial) formula to determine the characteristic vector of a new network G(N)(+), which is, approximately, the line digraph of N. We use this formula to obtain relations between some well-studied bit permutation networks. (C) 2001 John Wiley & Sons, Inc.