# Area complexity of multilective merging

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

## 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:
$$A\left( {n,m,k,r} \right) = \left\{ \begin{gathered}\Omega (\tfrac{n}{r}) for 2^k \geqslant \tfrac{n}{r} and n \geqslant m \geqslant \tfrac{n}{r} \hfill \\\Omega \left( {m\left( {\left( {\log \tfrac{n}{{rm}}} \right) + 1} \right)} \right) for 2^{\tfrac{3}{8}k} \geqslant \tfrac{n}{r} and \tfrac{n}{r} \geqslant m \hfill \\\Omega \left( {m\left( {\left( {\log \tfrac{{2^k }}{m}} \right) + 1} \right)} \right) for \tfrac{n}{r} \geqslant m and \tfrac{n}{r} \geqslant 2^{\tfrac{3}{8}k} and 2^{\left( {\tfrac{{3.\left( {8^K } \right) - 1}}{{8^{K + 1} - 1}}k} \right)} \geqslant m \hfill \\where K \geqslant 0 is the constant \hfill \\\end{gathered} \right.$$

## References

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