Skip to main content
Log in

A minimum-area circuit forl-selection

Algorithmica Aims and scope Submit manuscript

Abstract

We prove tight upper and lower bounds on the area of semelective, when-oblivious VLSI circuits for the problem ofl-selection. The area required to select thelth smallest ofn k-bit integers is found to be heavily dependent on the relative sizes ofl,k, andn. Whenl<2k, the minimal area isA = Θ(minn,l(k-logl)). Whenl≥2k,A = Θ(2k(logl-k + 1)).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Baudet, On the area required by VLSI circuits, inVLSI Systems and Computations (H. T. Kung, R. Sproull, and G. Steele, eds.), Computer Science Press, 1981, pp. 100–107.

  2. G. Bilardi, The area-time complexity of sorting, ACT-52, Ph.D. Dissertation, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1984.

  3. G. Bilardi, M. Pracchi, and F. P. Preparata, A critique of network speed in VLSI models of computation,IEEE J. Solid-State Circuits,17 (1982), 696–702.

    Article  Google Scholar 

  4. R. Brent and H. T. Kung, The area-time complexity of binary multiplication,J. Assoc. Comput. Mach.,28 (1981), 521–534.

    MATH  MathSciNet  Google Scholar 

  5. B. Chazelle and L. Monier, A model of computation for VLSI with related complexity results,Proceedings of the 13th Annual ACM Symposium on Theory of Computing, 1981, pp. 318–325.

  6. P. Duriš, O. Sýkora, C. Thompson, and I. Vrto, A lower bound on the area of DFT and DWHT circuits,Inform. Process. Lett.,21 (1985), 245.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Ďuriš, O. Sýkora, C. Thompson, and I. Vrto, A minimum-area circuit forl-selection, UCB/CSD 85/244, 1985, 13 pp.

  8. P. Ďuriš, O. Sýkora, C. Thompson, and I. Vrto, Tight chip area bounds for sorting,Comput. Artificial Intel.,4 (1985), 535–544.

    MATH  Google Scholar 

  9. R. Kolla, Where oblivious is not sufficient,Inform. Process. Lett.,17 (1983), 263–268.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. J. Lipton and R. Sedgewick, Lower bounds for VLSI,Proceedings of the 13th Annual ACM Symposium on Theory of Computing, 1981, pp. 300–307.

  11. C. A. Mead and M. Rem, Cost and performance of VLSI computing structures,IEEE J. Solid-State Circuits,14 (1979), 455–462.

    Article  Google Scholar 

  12. A. L. Rosenberg, References to the literature on VLSI algorithmics and related mathematical and practical issues,SIGACT News,16 (1984), 54–64.

    Google Scholar 

  13. J. Savage, Planar circuit complexity and the performance of VLSI algorithms, inVLSI Systems and Computations (H. T. Kung, R. Sproull, G. Steele, eds.), Computer Science Press, 1981, pp. 61–68.

  14. A. Siegel, Tight area bounds and provably goodAT 2 bounds for sorting circuits, Report Number 122, Courant Institute, New York University, 1984, 22 pp.

  15. A. R. Siegel, Minimum storage sorting networks,IEEE Trans. Comput.,34 (1985), 355–361.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. D. Thompson, The VLSI complexity of sorting,IEEE Trans. Comput.,32 (1983), 1171–1184.

    Article  MATH  Google Scholar 

  17. J. Ullman,Computational Aspects of VLSI, Computer Science Press, Rockville, MD, 1984.

    MATH  Google Scholar 

  18. I. Vrto, Optimal VLSI algorithms for selecting the maximum element of a set, inParcella 84: Proceedings of the Second International Workshop on Parallel Processing by Cellular Automata and Arrays (Wolfgang Händleret al., eds.), Akademie-Verlag, Berlin, 1985, pp. 232–239.

    Google Scholar 

  19. J. Vuillemin, A combinational limit to the computing power of VLSI circuits,IEEE Trans. Comput.,32 (1983), 294–300.

    Article  Google Scholar 

  20. A. C. Yao, The entropie limits of VLSI computations,Proceedings of the 13th Annual ACM Symposium on Theory of Computing, 1981, pp. 308–311.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Bernard Chazelle.

This work was supported in part by National Science Foundation Grant DMC 84-06408 and by the Slovak Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ďuriš, P., Sýkora, O., Thompson, C.D. et al. A minimum-area circuit forl-selection. Algorithmica 2, 251–265 (1987). https://doi.org/10.1007/BF01840362

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01840362

Key words

Navigation