The theory of connecting networks and their complexity: A review

Connecting networks are key subsystems of communications switching systems. This paper reviews what is known about the theoretical minimum complexity of connecting networks of several different types and presents the best known explicit constructions for them. In some cases, such as for strictly nonblocking connection networks, there is a significant difference between the best known construction and the theoretical minimum complexity. In other cases, such as for rearrangeably nonblocking connecting networks, the best construction differs from the minimum by only a constant.