In this paper, we studied the necessary and sufficient conditions for Banyan-type networks, which are rearrangeable nonblocking (RNB) by considering all possible degrees of crosstalk constraints. To the best of our knowledge, this paper is the first one to propose a comprehensive solution that takes into account of all the possible crosstalk constraints for optical interconnection network fabrics. Therefore, the necessary and sufficient RNB conditions for optical interconnection networks under various crosstalk constraints are defined completely. Moreover, we found the conditions are independent from the degree of crosstalk constraint. It means the number of needed planes will not increase due to a stricter constraint by allowing a lower degree of crosstalk unless it goes down to zero crosstalk. It also signifies that a much stricter degree of crosstalk constraint could be imposed without changing the hardware fabrics. These conditions provide the useful tips for a cost-effective design of such optical interconnection networks.

F.K. Hwang and S.C. Liaw (see IEEE/ACM Trans. Networking, vol.8, p.535-9, 2000) introduced a new nonblocking requirement for 2-cast traffic which imposes different requirements on different types of coexisting calls. The requirement is strictly nonblocking for point-to-point calls among the 2-cast traffic, and is rearrangeable for genuine 2-cast calls. We generalize the 2-cast calls to multicast calls and give a sufficient condition for such networks when the number of multicast calls is upper bounded.

In recent years, many multistage interconnection networks using 2 × 2 switching elements have been proposed for parallel architectures. Typical examples are baseline networks, banyan networks, shuffle-exchange networks, and their inverses. As these networks are blocking, such networks with extra stages have also been studied extensively. These include Benes networks and Δ ⊕ Δ′ networks. Recently, Hwang et al. studied k-extra-stage networks, which are a generalization of the above networks. They also investigated the equivalence issue among some of these networks. In this paper, we studied a more general class of networks, which we call (m + 1)-stage d-nary bit permutation networks. We characterize the equivalence of such networks by sequence of positive integers. © 1999 John Wiley & Sons, Inc. Networks 33: 261–267, 1999