Binomial Switching Networks for Concentration and Distribution

In this paper a new class of switching networks is presented for concentration and distribution interconnection assignments between disjoint sets of input and output terminals. These networks are called binomial switching networks because of their structural association with the binomial distribution. Binomial networks are uniform in that all connecting paths are of equal length and are such that cycles or iterations through stages of the network are not permitted, and binomial networks are rearrangeable in that implementing an additional path through the network for a new connection can require the rearranging of existing paths. It is shown that an upper bound on the number of such rearrangements is closely related to the number of stages in the network. A sparse crossbar switch construction of the binomial switching network is presented which contains crossbar switches in which it is not possible to connect each switch input to each switch output. Finally, the number of crosspoints needed for such networks for sufficiently large numbers of input and output terminals is seen to be less than the classical, benchmark alternatives for both concentration and distribution assignments.