Some topological properties of bitonic sorters

The paper proves some topological properties of bitonic sorters, which have found applications in constructing, along with banyan networks, internally nonblocking switching fabrics in future broadband networks. The states of all the sorting elements of an N×N bitonic sorter are studied for four different input sequences {a_i} _i=l^N, {b_i}_i=l^N, {c_i}_i=l^N, and {d_i}_i=l ^N where a_i=i-1, b_i=N-i, and the binary representations of c_i and d_i are the bit reverse of those of a_i and b_i, respectively. An application of these topological properties is to help design efficient fault diagnosis procedures. We present an example for detecting and locating a single faulty sorting element under a simple fault model where all sorting elements are always in the straight state or the cross state