On Optimal Merging Networks

  • Kazuyuki Amano
  • Akira Maruoka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


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.


Lower Bound Induction Hypothesis Induction Step Crucial Part Detailed Proof 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kazuyuki Amano
    • 1
  • Akira Maruoka
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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