Area complexity of multilective merging

  • Pavel Ferianc
  • Ondrej Sýkora
Submitted Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 505)


Lower bounds on the area A(n,m,k,r) required for merging of two sorted sequences of k-bit numbers with length n and m respectively, when the inputs can be replicated up to r times (rn), are given:
$$A\left( {n,m,k,r} \right) = \left\{ \begin{gathered}\Omega (\tfrac{n}{r}) for 2^k \geqslant \tfrac{n}{r} and n \geqslant m \geqslant \tfrac{n}{r} \hfill \\\Omega \left( {m\left( {\left( {\log \tfrac{n}{{rm}}} \right) + 1} \right)} \right) for 2^{\tfrac{3}{8}k} \geqslant \tfrac{n}{r} and \tfrac{n}{r} \geqslant m \hfill \\\Omega \left( {m\left( {\left( {\log \tfrac{{2^k }}{m}} \right) + 1} \right)} \right) for \tfrac{n}{r} \geqslant m and \tfrac{n}{r} \geqslant 2^{\tfrac{3}{8}k} and 2^{\left( {\tfrac{{3.\left( {8^K } \right) - 1}}{{8^{K + 1} - 1}}k} \right)} \geqslant m \hfill \\where K \geqslant 0 is the constant \hfill \\\end{gathered} \right.$$


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [U]
    Ullman, J.D., Computational Aspects of VLSI, Computer Science Press, Rockville, Md. 1983.Google Scholar
  2. [Sa]
    Savage, J.E., The Performance of Multilective VLSI Algorithms, in “Journal of Computer and System Sciences Vol. 29, No. 2, October 1984,” Academic Press, New York and London.Google Scholar
  3. [Si]
    Siegel, A., Tight Area Bounds and Provably Good AT 2 Bounds for Sorting Circuits. TR, CS Dept.,New York University, New York 1984.Google Scholar
  4. [G]
    Gubáš, X., Close properties of the communication and the area complexity of VLSI circuits (in Slovak), Master thesis, Comenius University, Bratislava 1988.Google Scholar
  5. [PSV]
    Palko,V., Sýkora,O., Vrťo,I., Area complexity of merging, In: MFCS' 89, Springer Verlag 1989, 390–396.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Pavel Ferianc
    • 1
  • Ondrej Sýkora
    • 1
  1. 1.Computing CentreSlovak Academy of SciencesBratislavaCzecho-Slovakia

Personalised recommendations