Ideas for Faster Networks

Abstract

We have already seen, in Chap. 9, that there is a gap in the number of steps between the fastest-known network and the information-theoretic lower bound. Thus, while trying to find a faster N-key sorting network , try to select a value for N for which this gap is the greatest. The initial steps of your network should combine all N keys into a single-segment poset. After that, apply the divide-and-conquer strategy described in Chap. 7 to split your keys into groups. As a consequence, the final steps of your network will contain a number of G-key sorting networks for some small, preferably even; G. The most difficult group will be the group in the middle. Thus, you may choose to place one group just below the mid-point and the other just above the mid-point. The other choice would be to place one group to straddle the mid-point with another group just below it and a third group just above it. Another approach to solving this problem would be using Sortnet commands. These commands help the designer select the comparators that: remove the most dashes from the Shmoo chart; affect the most cases; or a combination of both.