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

A bit permutation network is an s-stage interconnection network composed of dn−1 d × 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 sstage d-nary bit permutation network N with dn inputs (outputs) can be characterized by an (s − 1)-vector (k1, . . . , ks−1), where kt ∈ {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. © 2001 John Wiley & Sons, Inc.