Abstract. We propose a framework to analyze and compare wavelength division multiplexed (WDM) switching networks qualitatively and quantitatively. The framework not only help analyze and compare the complexity of WDM switching networks, but also explain interesting properties of different designs. Then, several important problems arising from this idea are addressed, and complexity bounds are derived. We also give several applications of the proposed model, including explicit constructions of non-blocking WDM switching fabrics. Key words. Wavelength division multiplexing, switching networks, ©������ �-connectors. AMS subject classifications. 05C75, 05C90, 05C35 1. Introduction. With

When analyzing a nonblocking switching network, the typical problem is to find a route for a new request through the network without disturbing existing routes. By solving this problem, we can derive how many hardware components of a certain type (Banyan planes in a multi-log network, for instance) are needed for the network to be nonblocking. This scenario appears in virtually all combinations of switching environments: strictly, widesense or rearrangeably nonblocking, unicast or multicast switching, and circuit, multirate, or photonic switching. In this paper, we show that the König-Egevary theorem is a very good tool which helps solve the above prototypical problem. The idea is to somehow “represent” the potential blocking connections as edges of a bipartite graph. The maximum number of blocking connections roughly corresponds to the size of a maximum matching in that bipartite graph. The size of any vertex cover, by the König-Egevary theorem, is an upper bound on the maximum number of blocking connections. Thus, by specifying a small vertex cover, we can derive the sufficient number of hardware components for the network to be nonblocking. We illustrate the technique by analyzing crosstalk-free and non-crosstalk-free widesense nonblocking multicast multi-log networks. Particularly, for the first time in the literature we derive conditions for the d-ary multi-log network to be