The generalized class of g-chain periodic sorting networks

A periodic sorter is a sorting network which is a cascade of a number of identical blocks, where output i of each block is input i of the next block. Previously, (Dowd et al., 1989) introduced the balanced merging network, with N=2^k inputs/outputs and log N stages of comparators. Using an intricate proof, they showed that a cascade of log N such blocks constitutes a sorting network. We have introduced a class of merging networks with N=2^k inputs/outputs and with periodic property (R. Becker et al., 1993). In this paper we extend our class of merging networks to arbitrary size N. For each N, the class contains an exponentially large number of merging networks (about 2^N/2-1) with [log N] stages. The balanced merger is one network in this class. Other networks use fewer comparators. A cascade of [log N] copies of a merging network in this class yields a periodic sorter. We provide a very simple and elegant proof of correctness based on the recursive structure of the networks