Area Complexity of Multilective Merging

  • Pavel Ferianc
  • Ondrej Sýkora
Part of the Lecture Notes in Computer Science book series (LNCS, volume 506)

Abstract

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:
$$A(n,m,k,r) = \left\{ {\begin{array}{*{20}{c}} {\Omega \left( {\frac{n}{r}} \right) for {2^k} \geqslant \frac{n}{r} and n \geqslant m \geqslant \frac{n}{r}} \\ {\Omega (m((\log \frac{{{2^k}}}{m}) + 1)) for {2^{\frac{3}{8}k}} \geqslant \frac{n}{r} and \frac{n}{r} \geqslant m} \\ {\Omega (m((\log \frac{{{2^k}}}{m}) + 1))for\frac{n}{r} \geqslant m and \frac{n}{r} \geqslant {2^{\frac{3}{8}k}} and {2^{(\frac{{3.({8^K}) - 1}}{{{3^{K + 1}} - 1}})}} \geqslant m} \end{array}} \right.$$

Keywords

Europe 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [U]
    Ullman, J.D., Computational Aspects of VLSI, Computer Science Press, Rockville, Md. 1983.MATHGoogle 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 AT2 Bounds for Sorting Circuits. TR, CS Dept.,New York University, New York 1984.Google Scholar
  4. [G]
    Gubâs, 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., Sÿkora, O., Vrto, 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