Large [ G,d] Sorting Networks

With only a few exceptions the minimum-comparator N-sorter networks employ the generalized "divide-sort-merge" strategy. That is, the N inputs are divided among g 2 2 smaller sorting networks -of size N1’N2’...‘Ng9 where N = g ck~1 Nk -that comprise the initial portion of the N-sorter network. The remainder of the N-sorter is a comparator network that merges the outputs of the Nl-, N2-, . . . . and N -sorter g networks into a single sorted sequence. The most economical merge networks yet designed, known as the M[g,d]' merge networks, consist of d smaller merge networks -where d is a common divisor of N1☺p l l l ,Ng -followed by a special comparator network labeled a "[g,d] f-network." In this paper we describe special constructions for [2r,2r] f-networks, r > 1, which enable us to reduce the number of comparators required by a large N-sorter network from .2pNm(log2N) 2 .25N(log2N) + O(N) to .27N(log2N)2 .37N(log2N) + O(N).