Switching networks serve as the core of network switches and routers, and communication subsystems of multiprocessor and multi-computer computing systems. There has been a growing interest in developing high-speed switches for multicasting. A wide class of applications, such as teleconferencing, video distribution, LAN bridging and distributed data processing, require multicasting communications. The essential network components for such applications are multicast switches. Rearrangeable nonblocking (RNB) multicast switching networks are used for packet switching, and strictly nonblocking (SNB) and wide-sense nonblocking (WSNB) multicast switching networks are used for circuit switching. Optimal RNB multicast switching networks have been constructed for a long time, and it was shown that the lower bound for the cost SNB multicast switching network is O(N^2) in 1980. Thus, for scalable circuit switching applications minimum-cost WSNB multicast switching networks are the only solution. Multicast networks (a.k.a. generalized connection networks, generalized connectors, distribution networks) were first formally introduced in English literature by Masson and Jordan in 1972. Until now, the WSNB multicast switching network with lowest cost remains to be Pippenger's network designed in 1973. It has been a general belief that Pippenger's network is very difficult to improve. One of the major goals of this proposed research is to seek WSNB multicast switching networks better than Pippenger's network. In addition, we also consider constructing optimal or near-optimal nonblocking multicast switching networks under routability and optical implementation constraints. All problems considered are constrained optimization problems with important implications. This proposed work not only has significant theoretical importance but is also of practical value. In the last 33 years, no progress on WSNB multicast switching networks better than Pippenger's network has been reported. The intellectual merit of the proposed research lies in the attempt of tackling a long-standing open theoretical problem, and its related problems arising in new network technologies.
