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Space Efficient Hash Tables with Worst Case Constant Access Time

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

We generalize Cuckoo Hashing [16] to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ∈) n memory cells, for any constant ∈ > 0. Assuming uniform hashing, accessing or deleting table entries takes at most d = O(ln 1/∈ ) probes and the expected amortized insertion time is constant. This is the first dictionary that has worst case constant access time and expected constant update time, works with (1+∈) n space, and supports satellite information. Experiments indicate that d = 4 choices suffice for ∈ ≈ 0.03. We also describe a hash table data structure using explicit constant time hash functions, using at most d = O(ln2 1/∈ ) probes in the worst case.

A corollary is an expected linear time algorithm for finding maximum cardinality matchings in a rather natural model of sparse random bipartite graphs.

This work was partially supported by DFG grant SA 933/1-1 and the Future and Emerging Technologies programme of the EU under contract number IST-1999- 14186 (ALCOM-FT).

The present work was initiated while this author was at BRICS, Aarhus University, Denmark.

Part of this work was done while the author was at MPII. 1 In this paper “whp.” will mean “with probability 1 - O(1/n)”.

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References

  1. R. P. Brent. Reducing the retrieval time of scatter storage techniques. Communications of the ACM, 16(2):105–109, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Z. Broder and A. R. Karlin. Multilevel adaptive hashing. In Proc. 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 43–53. ACM Press, 2000.

    Google Scholar 

  3. A. Brodnik and J. I. Munro. Membership in constant time and almost-minimum space. SIAM J. Comput., 28(5):1627–1640, 1999.

    Google Scholar 

  4. J. G. Cleary. Compact hash tables using bidirectional linear probing. IEEE Transactions on Computers, C-33(9):828–834, September 1984.

    Article  Google Scholar 

  5. M. Dietzfelbinger, J. Gil, Y. Matias, and N. Pippenger. Polynomial hash functions are reliable (extended abstract). In Proc. 19th International Colloquium on Automata, Languages and Programming, volume 623 of LNCS, pages 235–246. Springer-Verlag, 1992.

    Google Scholar 

  6. M. Dietzfelbinger and T. Hagerup. Simple Minimal Perfect Hashing in Less Space In Proc. 9th European Symposium on Algorithms, volume 2161 of LNCS, pages 109–120. Springer-Verlag, 2001.

    Google Scholar 

  7. M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, and R. E. Tarjan. Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738–761, 1994.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. G. H. Gonnet and J. I. Munro. Efficient ordering of hash tables. SIAM J. Comput., 8(3):463–478, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. E. Hopcroft and R. M. Karp. An O(n 5/2) algorithm for maximum matchings in bipartite graphs. SIAM J. Comput., 2:225–231, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. A. T. Maddison. Fast lookup in hash tables with direct rehashing. The Computer Journal, 23(2):188–189, May 1980.

    Article  Google Scholar 

  12. E. G. Mallach. Scatter storage techniques: A uniform viewpoint and a method for reducing retrieval times. The Computer Journal, 20(2):137–140, May 1977.

    Article  MATH  Google Scholar 

  13. M. Matsumoto and T. Nishimura. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACMTMCS: ACM Transactions on Modeling and Computer Simulation, 8:3–30, 1998.

    Article  MATH  Google Scholar 

  14. R. Motwani. Average-case analysis of algorithms for matchings and related problems. J. ACM, 41(6):1329–1356, November 1994.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Pagh. Low redundancy in static dictionaries with constant query time. SIAM J. Comput., 31(2):353–363, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Pagh and F. F. Rodler. Cuckoo hashing. In Proc. 9th European Symposium on Algorithms, volume 2161 of LNCS, pages 121–133. Springer-Verlag, 2001.

    Google Scholar 

  17. R. Raman and S. Srinivasa Rao. Dynamic dictionaries and trees in near-minimum space. Manuscript, 2002.

    Google Scholar 

  18. R. L. Rivest. Optimal arrangement of keys in a hash table. J. ACM, 25(2):200–209, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  19. P. Sanders. Asynchronous scheduling of redundant disk arrays. In 12th ACM Symposium on Parallel Algorithms and Architectures, pages 89–98, 2000.

    Google Scholar 

  20. P. Sanders. Reconciling simplicity and realism in parallel disk models. In 12th ACM-SIAM Symposium on Discrete Algorithms, pages 67–76, 2001.

    Google Scholar 

  21. P. Sanders, S. Egner, and J. Korst. Fast concurrent access to parallel disks. In 11th ACM-SIAM Symposium on Discrete Algorithms, pages 849–858, 2000.

    Google Scholar 

  22. A. Yao. Uniform hashing is optimal. J. ACM, 32(3):687–693, 1985.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Dimitris Fotakis & Peter Sanders

  2. IT University of Copenhagen, Denmark

    Rasmus Pagh

  3. Computer Technology Institute (CTI), Greece

    Paul Spirakis

Authors
  1. Dimitris Fotakis
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  2. Rasmus Pagh
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  3. Peter Sanders
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  4. Paul Spirakis
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Fotakis, D., Pagh, R., Sanders, P., Spirakis, P. (2003). Space Efficient Hash Tables with Worst Case Constant Access Time. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_25

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  • DOI: https://doi.org/10.1007/3-540-36494-3_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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