Wide-sense and strict-sense nonblocking operation of multicast multi-log/sub 2/ n switching networks

Multicast connections are used in broad-band switching networks as well as in parallel processing. We consider wide-sense and strict-sense nonblocking conditions for multi-log/sub 2/ N switching networks with multicast connections. We prove that such networks are wide-sense nonblocking if they are designed by vertically stacking at least t /spl middot/ 2/sup n-t-1/ + 2 /sup n-2t-1/ planes of a log/sub 2/ N networks together, where 1 /spl les/ t /spl les/ [n/2] and t defines the size of a blocking window K = 2/sup t/. For t = [n/2] and n even, and for [n/2] /spl les/ t /spl les/ n the number of planes must be at least t /spl middot/ 2/sup n-t-1/ + 1 and 2/sup t/ + (n - t - 1) /spl middot/ 2/sup n-t-1/ - 2/sup 2t-n-1/ + 1, respectively. In the case of strict-sense nonblocking switching networks, the number of planes is at least N/2. The results obtained in this paper show that in many cases number of planes in wide-sense nonblocking switching networks is less than those for t = [n/2] considered by Tscha and Lee (see ibid., vol.47, p.1425-31, Sept. 1999). The number of planes given in the paper is the minimum number of planes needed for wide-sense nonblocking operation provided that Algorithm 1 is used for setting up connections. The minimum number of planes for such operation in general is still open issue.