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A New Trade-Off for Deterministic Dictionaries

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Algorithm Theory - SWAT 2000 (SWAT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

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Abstract.

We consider dictionaries over the universe U = 0,1w on a unit-cost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n)O(1) and updates in time (log n)O(1), where n is the size of the set stored. This is the first such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c)) for a constant c<1.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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References

  1. Arne Andersson and Mikkel Thorup. Tight(er) worst-case bounds on dynamic searching and priority queues. In Proceedings of the 32th Annual ACM Symposium on Theory of Computing (STOC 2000), New York, 2000. ACM Press.

    Google Scholar 

  2. Paul Beame and Faith Fich. Optimal bounds for the predecessor problem. In Proceedings of the 31th Annual ACM Symposium on Theory of Computing (STOC’ 99 ), pages 295–304, New York, 1999. ACM Press.

    Google Scholar 

  3. Martin Dietzfelbinger, Joseph Gil, Yossi Matias, and Nicholas Pippenger. Polynomial hash functions are reliable (extended abstract). In Proceedings of the 19th International Colloquium on Automata, Languages and Programming (ICALP’ 92), volume 623 of Lecture Notes in Computer Science, pages 235–246, Berlin, 1992. Springer-Verlag.

    Google Scholar 

  4. Martin Dietzfelbinger, Anna Karlin, Kurt Mehlhorn, Friedhelm Meyer Auf Der Heide, Hans Rohnert, and Robert E. Tarjan. Dynamic perfect hashing: Upper and lower bounds. SIAM Journal on Computing, 23(4):738–761, August 1994.

    Article  MATH  MathSciNet  Google Scholar 

  5. Martin Dietzfelbinger and Friedhelm Meyer Auf der Heide. A new universal class of hash functions and dynamic hashing in real time. In Automata, languages and programming (Coventry, 1990), pages 6–19. Springer, New York, 1990.

    Chapter  Google Scholar 

  6. James R. Driscoll, Neil Sarnak, Daniel D. Sleator, and Robert E. Tarjan. Making data structures persistent. J. Comput. System Sci., 38(1):86–124, 1989. 18th Annual ACM Symposium on Theory of Computing (Berkeley, CA, 1986).

    Article  MATH  MathSciNet  Google Scholar 

  7. Michael L. Fredman, János Komlós, and Endre Szemerédi. Storing a sparse table with O(1) worst case access time. J. Assoc. Comput. Mach., 31(3):538–544, 1984.

    MATH  MathSciNet  Google Scholar 

  8. Michael L. Fredman and Dan E. Willard. Surpassing the information-theoretic bound with fusion trees. J. Comput. System Sci., 47:424–436, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  9. Torben Hagerup. Sorting and searching on the word RAM. In Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science (STACS’ 8 ), pages 366–398. Springer, Berlin 1998.

    Google Scholar 

  10. Torben Hagerup. Fast deterministic construction of static dictionaries. In Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA1999), pages 414–418, New York, 1999. ACM.

    Google Scholar 

  11. Peter Bro Miltersen. Error correcting codes, perfect hashing circuits, and deterministic dynamic dictionaries. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1998), pages 556–563, New York, 1998. ACM.

    Google Scholar 

  12. Rasmus Pagh. Faster deterministic dictionaries. In Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), pages 487–493, New York, 2000. ACM.

    Google Scholar 

  13. R. Sundar. A lower bound on the cell probe complexity of the dictionary problem. Manuscript, 1993.

    Google Scholar 

  14. P. van Emde Boas. Preserving order in a forest in less than logarithmic time. In 16th Annual Symposium on Foundations of Computer Science (Berkeley, Calif., (1975), pages 75–84, Long Beach, Calif., 1975. IEEE Computer Society.

    Google Scholar 

  15. Andrew Chi Chih Yao. Should tables be sorted? J. Assoc. Comput. Mach., 28(3):615–628, 1981.

    MATH  MathSciNet  Google Scholar 

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Pagh, R. (2000). A New Trade-Off for Deterministic Dictionaries. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_4

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  • DOI: https://doi.org/10.1007/3-540-44985-X_4

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  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

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