Large [g,d] sorting networks

• Authors: David C. Van Voorhis
• Venue: Large [g,d] sorting networks
• Year: 1971

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 $\geq$ 2 smaller sorting networks -- of size $N_1,N_2,...,N_g$, where $N = \sum_{k=1}^{g} N_k$ -- 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 $N_1-, N_2-, ...,$ and $N_g$-sorter networks into a single sorted sequence. The most economical merge networks yet designed, known as the "[g,d]" merge networks, consist of d smaller merge networks -- where d is a common divisor of $N_1,N_2,...,N_g$ -- followed by a special comparator network labeled a "[g,d] f-network." In this paper we describe special constructions for $[2^r,2^r]$ f-networks, r