A new universal class of hash functions and dynamic hashing in real time

  • Martin Dietzfelbinger
  • Friedhelm Meyer auf der Heide
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 443)


The paper presents a new universal class of hash functions which have many desirable features of random functions, but can be (probabilistically) constructed using sublinear time and space, and can be evaluated in constant time.

These functions are used to construct a dynamic hashing scheme that performs in real time, i.e., a Monte Carlo type dictionary that uses linear space and needs worst case constant time per instruction. Thus instructions can be given in constant length time intervals. Answers to queries given by the algorithm are always correct, the space bound is always satisfied, and the algorithm fails only with probability O(nk), where n is the number of data items currently stored. The constant k can be chosen arbitrarily large.


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  1. [AL86]
    Aho, H. V., and Lee, D., Storing a dynamic sparse table, Proc. of the 27th IEEE FOCS, 1986, pp. 55–60.Google Scholar
  2. [AV79]
    Angluin, D., and Valiant, L. G., Fast probabilistic algorithms for Hamiltonian circuits and matchings, J. Comput. Syst. Sci. 18 (1979), 155–193.Google Scholar
  3. [BK88]
    Brassard, G., and Kannan, S., The generation of random permutations on the fly, IPL 28 (1988) 207–212.Google Scholar
  4. [DKM88]
    Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., and Tarjan, R. E., Dynamic perfect hashing: Upper and lower bounds, Proc. of the 29th IEEE FOCS, 1988, pp. 524–531; also: Tech. Report No. 282, Fachbereich Informatik, Universität Dortmund, 1988.Google Scholar
  5. [DM89]
    Dietzfelbinger, M., and Meyer auf der Heide, F., An optimal parallel dictionary, Proc. of ACM Symp. on Parallel Algorithms and Architectures, 1989, pp. 360–368.Google Scholar
  6. [DM90]
    Dietzfelbinger, M., Meyer auf der Heide, F., How to distribute a dictionary in a complete network, Proceedings of the 22nd ACM STOC, 1990.Google Scholar
  7. [FKS84]
    Fredman, M. L., Komlós, J., and Szemerédi, E., Storing a sparse table with O(1) worst case access time, J. ACM 31(3), 1984, 538–544.Google Scholar
  8. [GMW90]
    Gil, J., Meyer auf der Heide, F., and Wigderson, A., Not all keys can be hashed in constant time, Proc. of the 22nd ACM STOC, 1990.Google Scholar
  9. [Hof87]
    Hofri, M., Probabilistic Analysis of Algorithms, Springer Verlag, New York, 1987.Google Scholar
  10. [KU86]
    Karlin, A., and Upfal, E., Parallel hashing — an efficient implementation of shared memory, Proc. of the 18th ACM STOC, 1986, pp. 160–168.Google Scholar
  11. [KRS90]
    Kruskal, C. P., Rudolph, L., and Snir, M., A complexity theory of efficient parallel algorithms, Proc. of 15th ICALP, 1988, pp. 333–346, Springer LNCS 317; also: revised preprint.Google Scholar
  12. [LN89]
    Lipton, R.J., and Naughton, J.G. Clocked adversaries for hashing, Tech. Rep. CS-TR-203-89, Princeton, 1989.Google Scholar
  13. [Meh84]
    Mehlhorn, K., Data Structures and Algorithms, Vol. 1, 1984, Springer Verlag, Berlin.Google Scholar
  14. [MV84]
    Mehlhorn, K., and Vishkin, U., Randomized and deterministic simulations of PRAMs by parallel machines with restricted granularity of parallel memory, Acta Informatica 21, 1984, 339–374.Google Scholar
  15. [Ran87]
    Ranade, A. G., How to emulate shared memory, Proc. of the 28th IEEE FOCS, 1987, pp. 185–194.Google Scholar
  16. [Sie89]
    Siegel, A., On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications, Proc. of the 30th IEEE FOCS, 1989, pp. 20–25.Google Scholar
  17. [Upf84]
    Upfal, E., Efficient schemes for parallel communication, J. ACM 31(3), 1984, 507–517.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Martin Dietzfelbinger
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  1. 1.Fachbereich 17 · Mathematik — InformatikUniversität-GH PaderbornPaderbornFed. Rep. of Germany

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