A unified algebraic theory of sorting, routing, multicasting, and concentration networks
Shuo-Yen Robert Li · 2012
Sorters, concentrators, mergers, inserters, and other sorting-style devices are widely applied to communications and computation. A sorter receives input values belonging to an ordered set and permutes them into the monotonic order. It is a special form of a unicast switch where the selection of the I/O connection pattern is determined by the comparison among signal values. In particular, a sorting cell means a 2×2 sorter with just two available I/O connection patterns, called the bar and cross states.