Nonblocking conditions for multi-log2 N multiconnection networks

The multi-log₂ N network is an abstract parallel switch architecture which possesses many desirable characteristics for high-speed electronics and nonlogic photonic switches, such as fault-tolerance, log₂ N stages between each inlet-outlet pair, almost zero crosstalk, self-routing capability, etc. The conditions for rearrangeable nonblocking and for strictly nonblocking multi-log₂ N multiconnection networks, which have been open problems, are presented. It is shown that the same nonblocking conditions hold regardless of whether the multi-log ₂ N networks deploy one-to-one connections or multiconnections. The recently proposed UMSR (unified multiconnection-segmenting rule) and CIG (connection-intersection graph) allow one to ease the analysis of intersecting multiconnections in the network. In particular, the concept of the virtual degree of a CIG facilitates characterization of the nonblocking conditions for the multi-log₂ N multiconnection networks