Load-balanced switches have received a lot of attention lately as they are much more scalable than other existing switch architectures in the literature. One of the most salient features of load-balanced switches is its simplicity of implementing deterministic and periodic connection patterns for the switch fabrics. In particular, for an N × N load-balanced switch, its switch fabric only needs an N × N rotator that is capable of realizing all the powers of the circular shift permutation. In this paper, we consider the problem of incremental update of the number of linecards in load-balanced switches. For this, our idea is to consider a 2M× 2Mdegenerated banyan network that only uses half of the 2M+1inputs/outputs in the classical 2M+1× 2M+1banyan network. We show how one can use the 2M× 2Mdegenerated banyan network as a p × p rotator for any 2 ≤ p ≤ 2M. This is done by a specific rule of placing the p linecards in the 2Minput/output ports of the 2M× 2Mdegenerated banyan network. In special, when p = 2M, the 2M× 2Mdegenerated banyan network can also be used as a crosstalk-free 2M× 2Mrotator, where all the routing paths do not share a common node. As such, one can use a 2M+1× 2M+1banyan network as the switch fabric for a 2M× 2Mload-balanced switch that is capable of providing incremental update of the number of linecards.

Inspired by the recent development of optical queueing theory, in this paper we study a class of multistage interconnection networks (MINs), called twister networks. Unlike the usual recursive constructions of MINs (either by two-stage expansion or by three-stage expansion), twister networks are constructed directly by a concatenation of bipartite networks. Moreover, the biadjacency matrices of these bipartite networks are sums of subsets of the powers of the circular shift matrix. Though MINs have been studied extensively in the literature, we show there are several distinct properties for twister networks, including routability and conditionally nonblocking properties. In particular, we show that a twister network satisfying (Al) in the paper is routable, and packets can be self-routed through the twister network by using the C-transform developed in optical queueing theory. Moreover, we define an N -modulo distance and use it to show that a twister network satisfying (A2) in the paper is conditionally nonblocking if the N-modulo distance between any two outputs is not greater than two times of the N-modulo distance between the corresponding two inputs. Such a conditionally nonblocking property allows us to show that a twister network with N inputs/outputs can be used as a p × p rotator and a p × p symmetric TDM switch for any 2 ¿ p ¿ N. As such, one can use a twister network as the switch fabric for a two-stage load balanced switch that is capable of providing incremental update of the number of linecards.