Crosstalk-free Rearrangeable Multistage Interconnection Networks

In this paper, the notion of crosstalk-free rearrangeability (CFrearrangeability) of multistage interconnection networks (MINs) is formally defined. Using the concept of line digraphs from graph theory, we show that the problem of crosstalk-free routing on any bit permutation network (BPN) is always equivalent to the classical permutation routing problem on a BPN of smaller size and with fewer stages. We also show the CF-rearrangeability and minimality (in stage number) of three families of BPNs, including the dilated Benes network. Some necessary conditions for a BPN to be CF-rearrangeable are given, and a brief discussion of CF-rearrangeable networks with dilation in time or space is included.