Yet another result on multi-log2N networks

One-to-many connection (i.e., multicast) is an important communication primitive used in parallel processing and high-speed switching in order to simultaneously send data from an input to more than one output. We prove that for even (respectively, odd) n, a multi-log₂N network is strictly nonblocking for a one-to-many connection traffic if it is designed by vertically stacking at least (δn)/4+1((δ/2)(n-1)+1) planes of a log₂N network together, where N=2ⁿ, δ=2^[n/2], and [x] denotes the greatest integer less than or equal to x. We thus give answer to the open problem and introduce yet another strictly nonblocking multicast network. The characterized network has self-routing capability, regular topology, O(2log₂N+2log₂(log₂N)) stages, and fewer crosspoints than the Clos network for N⩾512. We then extend multi log₂N multicast networks to the fanout restricted nonblocking networks. It turns out that the multi-log₂N network nonblocking in a strict-sense for a one-to-one connection traffic is also wide-sense nonblocking for a multicast traffic in which the fanout of any connection does not exceed δ, provided that for even (respectively, odd) n, the fanout capability of each log₂N network is restricted to stage (n/2)(((n-1)/2)+1) through n-1