Skip to main content
SpringerLink
Log in

Membership in constant time and minimum space

  • Conference paper
  • First Online:
Book cover Algorithms — ESA '94 (ESA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

Included in the following conference series:

Abstract

We investigate the problem of storing a subset of the elements of a bounded universe so that searches can be performed in constant time and the space used is within a constant factor of the minimum required. Initially we focus on the static version of this problem and conclude with an enhancement that permits insertions and deletions.

This research was supported in part by the Natural Science and Engineering Research Council of Canada under grant number A-8237 and the Information Technology Research Centre of Ontario.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Dietzfelbinger, J. Gil, Y. Matias, and N. Pippenger. Polynomial hash functions are reliable. In Proceedings 19 th International Colloquium on Automata, Languages and Programming, volume 623 of Lecture Notes in Computer Science, pages 235–246. Springer-Verlag, 1992.

    Google Scholar 

  2. M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, and R.E. Tarjan. Dynamic perfect hashing: Upper and lower bounds. In 29 th IEEE Symposium on Foundations of Computer Science, pages 524–531, 1988.

    Google Scholar 

  3. M. Dietzfelbinger and F. Meyer auf der Heide. A new universal class of hash functions and dynamic hashing in real time. In Proceedings 17 th International Colloquium on Automata, Languages and Programming, volume 443 of Lecture Notes in Computer Science, pages 6–19. Springer-Verlag, 1990.

    Google Scholar 

  4. P. Elias. Efficient storage retrieval by content and address of static files. Journal of the ACM, 21(2):246–260, April 1974.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Elias and R.A. Flower. The complexity of some simple retrieval problems. Journal of the ACM, 22(3):367–379, July 1975.

    Article  MathSciNet  Google Scholar 

  6. P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, chapter 1, pages 1–66. Elsevier, Amsterdam, Holland, 1990.

    Google Scholar 

  7. A. Fiat and M. Naor. Implicit O(1) probe search. SIAM Journal on Computing, 22(1):1–10, 1993.

    Article  MathSciNet  Google Scholar 

  8. A. Fiat, M. Naor, J.P. Schmidt, and A. Siegel. Nonoblivious hashing. Journal of the ACM, 39(4):764–782, October 1992.

    Article  MathSciNet  Google Scholar 

  9. M.L. Fredman, J. Komlós, and E. Szemerédi. Storing a sparse table with O(1) worst case access time. Journal of the ACM, 31(3):538–544, July 1984.

    Article  Google Scholar 

  10. M.L. Fredman and M.E. Saks. The cell probe complexity of dynamic data structures. In 21 st ACM Symposium on Theory of Computing, pages 345–354, Seattle, Washington, 1989.

    Google Scholar 

  11. H.N. Gabow and R.E. Tarjan. A linear-time algorithm for a special case of disjoint set union. Journal of Computer and System Sciences, 30:209–221, 1985.

    Article  MathSciNet  Google Scholar 

  12. T. Hagerup, K. Mehlhorn, and J.I. Munro. Optimal algorithms for generating discrete random variables with changing distributions. In Proceedings 20th International Colloquium on Automata, Languages and Programming, volume 700 of Lecture Notes in Computer Science, pages 253–264. Springer-Verlag, 1993.

    Google Scholar 

  13. P.B. Miltersen. The bit probe complexity measure revisited. In Proceedings 10 th Symposium on Theoretical Aspects of Computer Science, volume 665 of Lecture Notes in Computer Science, pages 662–671. Springer-Verlag, 1993.

    Google Scholar 

  14. R.E. Tarjan and A.C. Yao. Storing a sparse table. Communications of the ACM, 22(11):606–611, November 1979.

    Article  MathSciNet  Google Scholar 

  15. A.C.-C. Yao. Should tables be sorted? Journal of the ACM, 28(3):614–628, July 1981.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L3G1, Waterloo, Ontario, Canada

    Andrej Brodnik & J. Ian Munro

Authors
  1. Andrej Brodnik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ian Munro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jan van Leeuwen

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brodnik, A., Munro, J.I. (1994). Membership in constant time and minimum space. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049398

Download citation

  • DOI: https://doi.org/10.1007/BFb0049398

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation