On Optimal Merging Networks

Abstract

We prove that Batcher’s odd-even (m,n)-merging networks are exactly optimal for (m,n)=(3,4k+2) and (4,4k+2) for k ≥ 0 in terms of the number of comparators used. For other cases where m ≤ 4, the optimality of Batcher’s (m,n)-merging networks has been proved. So we can conclude that Batcher’s odd-even merge yields optimal (m,n)-merging networks for every m ≤ 4 and for every n. The crucial part of the proof is characterizing the structure of optimal (2,n)-merging networks.