A 16-Key Sorting Network

Abstract

We analyzed Van Voorhis 16-key network because it is faster than the merge-sorting networks for 16 keys (9 steps instead of 10 steps). To help better understand the behavior of this network, we used the relabeling technique. We re-labeled the network by exchanging K[3] with K[8] and by exchanging K[7] with K[12]. This, resulted in a more logical placement of the 14 keys in the three sets between K[0] and K[15] since it put: K[11] through K[14] in the top set; K[5] through K[10] in the middle set; and K[1] through K[4] in the bottom set. When we drew the Knuth diagram for the re-labeled network , we found that: the first six steps partition the keys into four 4-key groups with every key in each group less than or equal to every key in the next higher group; steps 5 through 8 sort the keys within each group; and step 9 finishes sorting all the remaining cases to complete the sort of all 16 keys. Thus, relabeling this network helped us realize that it uses the well-known divide-and-conquer strategy to sort the 16 input leys.