Notes on merging networks (Prelimiary Version)
Zhu Hong, Robert Sedgewick · 1982
Several new results which contribute to the understanding of parallel merging networks are presented. First, a simple new explanation of the operation of Batcher's merging networks is offered. This view leads to the derivation of a modified version of Batcher's odd-even (m, n) network which has delay time [log(m+n)]. This is the same delay time as Batcher's bitonic (m, n) network, but it is achieved with substantially fewer comparators. Second, a correspondence is demonstrated between the number of comparators (and the delay time) for such networks and certain properties of binary number systems which have recently been extensively studied. Third, the [log(m + n)] delay time is shown to be optimal for a non-degenerate range of values of m and n.