The periodic balanced sorting network

A periodic sorting network consists of a sequence of identical blocks. In this paper, the periodic balanced sorting network, which consists of log <italic>n</italic> blocks, is introduced. Each block, called a balanced merging block, merges elements on the even input lines with those on the odd input lines. The periodic balanced sorting network sorts <italic>n</italic> items in <italic>O</italic>([log <italic>n</italic>]<supscrpt>2</supscrpt>) time using (<italic>n</italic>/2)(log <italic>n</italic>)<supscrpt>2</supscrpt> comparators. Although these bounds are comparable to many existing sorting networks, the periodic structure enables a hardware implementation consisting of only one block with the output of the block recycled back as input until the output is sorted. An implementation of our network on the shuffle exchange interconnection model in which the direction of the comparators are all identical and fixed is also presented.