Recursive construction of parallel distribution networks

Unified theory on preservation of conditionally non‐blocking switches by the two‐stage interconnection network

“…In this sense, they are actually more natural versions than the plain one. In fact, they are known to preserve several types of conditionally non-blocking switches [8,[16][17][18], while the plain version is not known to preserve any.…”

“…One application of a CU non-blocking switch is to serve as a circular-unimodal distributor [17], which is a switch under the 'distributor style' of in-band control and can be used in the recursive construction of self-routing distribution networks [18]. Meanwhile, a CU non-blocking switch under the sorting-style control constructs a circular sorter (Section 6.2.2 of [8]), which sorts input signal values into the ascending order subject to the constraint that the input values form a unimodal function of the circular input addresses.…”

“…One application of a CU non‐blocking switch is to serve as a circular‐unimodal distributor [17], which is a switch under the ‘distributor style’ of in‐band control and can be used in the recursive construction of self‐routing distribution networks [18].…”

Emulation of multistage interconnection networks by fibre memory

“…Meanwhile, the 2-stage network 2X(m, n) = S(m, n) + X(n, m) preserves several classes of 'conditionally non-blocking' switches, including 'unimodal-circular non-blocking' switches [11,17] and 0-1 'sorters' [11]. Symmetrically the 2-stage network X2(n, m) = X(n, m) + S(m, n) also preserves several classes of conditionally non-blocking switches, including 'circular-unimodal non-blocking switches' [11], 'circular sorters' [11] and 'circular-unimodal distributors' [18]. A 2 n × 2 n 'banyan-type network' is an n-stage MIN such that every stage consist of 2 n−1 2 × 2 nodes and every network input is connectable to every network output.…”