Nonblocking Conditions for Multi-Log2N Multiconnection Networks

초록

The multi-log2N network is an abstract parallel switch architecture which possesses many desirable characteristics for high-speed electronics and nonlogic photonic switches-such as fault-tolerance, log2N stages between each inlet-outlet pair, almost zero-crosstalk, and self-routing capability, etc. In this paper we present the conditions respectively for rearrangeable nonblocking and strictly nonblocking multi-log2N multiconnection networks which have been open problems[1-4]. Astonishingly, it is shown that the same nonblocking conditions hold regardless of whether the multi-log2N networks deploy one-to-one connections or multiconnections. The newly proposed UMSR(Unified Multiconnection-Segmenting Rule) and CIG(Connection-Intersection Graph) allow to ease the analysis of intersecting multiconnections in the network. In particular the concept called Virtual Degree of a CIG facilitates characterization of the nonblocking conditions for the muli-log2N multiconnection networks.