On Optimal Merging Networks
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.
KeywordsLower Bound Induction Hypothesis Induction Step Crucial Part Detailed Proof
Unable to display preview. Download preview PDF.
- 2.Batcher, K.E.: Sorting Networks and Their Applications. Proc. AFIPS 1968 SJCC 32, 307–314 (1968)Google Scholar
- 4.Knuth, D.E.: The Art of Computer Programming, 2nd edn. Sorting and Searching, vol. 3. Addison-Wesley, Reading (1998)Google Scholar
- 5.Leighton, T., Ma, Y., Suel, T.: On Probabilistic Networks for Selection, Merging, and Sorting. In: Proc. 7th Symp. Parallel Algorithms and Architectures, pp. 106–118 (1995)Google Scholar
- 7.Yamazaki, K., Mizuno, H., Masuda, K., Iwata, S.: Minimum Number of Comparators in (6,6)-merging Network. IEICE Trans. Inform. Syst. E83-D, 137–141 (2000)Google Scholar