Strictly Nonblocking Function-Cast d-Ary Multi-Log Networks under Fanout and Crosstalk Constraints

We derive conditions which are both necessary and sufficient for the d-ary multi-log switching networks to be f-cast strictly nonblocking under all combinations of fanout and crosstalk constraints. The fanout constraint tells us which stage(s) of the networks has fanout capability. The crosstalk constraint tells us whether or not two routes are allowed to share a link, or are allowed to share a switching element (crosstalk-free or not). The most novel contribution of this paper is the analytical technique, which combines an algebraic view of the d-ary multi-log network with the max-flow min-cut theorem. Our results are more general than previously known results on several fronts: (a) d-ary networks are more general than binary networks, (b) f-cast covers both unicast (f = 1) and broadcast (f = N), (c) both link-blocking and node-blocking are considered in a unified manner, and (d) all combinations of fanout constraints are considered.