# 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

Circuit State Area Complexity F233 Versus Determinate Schedule Tight Lower Bound
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

1. [U]
Ullman, J.D., Computational Aspects of VLSI, Computer Science Press, Rockville, Md. 1983.
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