Combinatorica

, Volume 13, Issue 1, pp 83–96 | Cite as

More analysis of double hashing

  • George S. Lueker
  • Mariko Molodowitch
Article

Abstract

In [8], a deep and elegant analysis shows that double hashing is asymptotically equivalent to the ideal uniform hashing up to a load factor of about 0.319. In this paper we show how a randomization technique can be used to develop a surprisingly simple proof of the result that this equivalence holds for load factors arbitrarily close to 1.

AMS subject Classification Code (1991)

68 Q 25 68 P 10 11 B 25 

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References

  1. [1]
    Miklós Ajtai, János Komlós, andEndre Szemerédi: There Is No Fast Single Hashing Algorithm,Information Processing Letters 7 (1978), 270–273.Google Scholar
  2. [2]
    Béla Bollobás, Andrei Z. Broder andIstvan Simon: The Cost Distribution of Clustering in Random Probing,J. ACM 37 (1990), 224–237.Google Scholar
  3. [3]
    G. H. Gonnet andR. Baeza-Yates:Handbook of Algorithms and Data Structures: In Pascal and C, Second Edition, Addison-Wesley, Wokingham, England, 1991.Google Scholar
  4. [4]
    Wassily Hoeffding: Probability Inequalities for Sums of Bounded Random Variables,J. American Statistical Association 58 (1963), 13–30.Google Scholar
  5. [5]
    Kumar Jog-Dev andS. M. Samuels: Monotone Convergence of Binomial Probabilities and a Generalization of Ramanujan's Equation,The Annals of Mathematical Statistics 39 (1968), 1191–1195.Google Scholar
  6. [6]
    János Komlós: Private communication, 1986.Google Scholar
  7. [7]
    Leo J. Guibas: Private communication, Fall 1987.Google Scholar
  8. [8]
    Leo J. Guibas andEndre Szemerédi: The Analysis of Double Hashing,Journal of Computer and System Sciences 16 (1978), 226–274.Google Scholar
  9. [9]
    Narendra Karmarkar andRichard M. Karp: The Differencing Method of Set Partititoning, Report No. UCB/CSD 82/113, Computer Science Division (EECS), University of California, Berkeley, December 1982.Google Scholar
  10. [10]
    D. Knuth:The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, Mass., 1973.Google Scholar
  11. [11]
    George S. Lueker andMariko Molodowitch: More Analysis of Double Hashing,Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, IL, May 1988, 354–359.Google Scholar
  12. [12]
    Nicholas Pippenger: Private communication, January 1988.Google Scholar
  13. [13]
    Jeanette P. Schmidt andAlan Siegel: On Aspects of the Universality and Performance for Closed Hashing,Proc. 21st Annual ACM Symposium on Theory of Computing, Seattle, WA, May 1989, 355–366.Google Scholar
  14. [14]
    Jeffrey D. Ullman: A Note on the Efficiency of Hash Functions,Journal of the ACM 19 (1972), 569–575.Google Scholar
  15. [15]
    Andrew C. Yao: Uniform Hashing Is Optimal,Journal of the ACM 32 3 (1985), 687–693.Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • George S. Lueker
    • 1
  • Mariko Molodowitch
    • 2
  1. 1.Department of Information and Computer ScienceUniversity of California, IrvineIrvineUSA
  2. 2.California State University, FullertonFullertonUSA

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