The Cell Probe Complexity of Succinct Data Structures

  • Anna Gál
  • Peter Bro Miltersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)

Abstract

We show lower bounds in the cell probe model for the redundancy/query time tradeoff of solutions to static data structure problems.

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References

  1. 1.
    M. Ajtai. A lower bound for finding predecessors in Yao’s cell probe model. Combinatorica, 8:235–247, 1988.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    N. Alon, O. Goldreich, J. Håstad, R. Peralta: Simple constructions of almost kwise independent random variables. Random Structures and Algorithms 3 (1992), 289–304.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    O. Barkol and Y. Rabani, Tighter bounds for nearest neighbor search and related problems in the cell probe model. In Proc. 32th Annual ACM Symposium on Theory of Computing (STOC’00), pages 388–396.Google Scholar
  4. 4.
    A. Borodin, R. Ostrovsky, Y. Rabani, Lower bounds for high dimensional nearest neighbor search and related problems. In Proc. 31th Annual ACM Symposium on Theory of Computing (STOC’99), pages 312–321.Google Scholar
  5. 5.
    A. Brodnik and J.I. Munro. Membership in constant time and almost-minim um space. SIAM Journal on Computing, 28:1627–1640, 1999.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    H. Buhrman, P.B. Miltersen, J. Radhakrishnan, S. Venkatesh. Are bitvectors optimal? In Proc. 32th Annual ACM Symposium on Theory of Computing (STOC’00), pages 449–458.Google Scholar
  7. 7.
    A. Chakrabarti, B. Chazelle, B. Gum, and A. Lvov. A lower bound on the complexity of approximate nearest-neighbor searching on the Hamming Cube. In Proc. 31th Annual ACM Symposium on Theory of Computing (STOC’99), pages 305–311.Google Scholar
  8. 8.
    E.D. Demaine and A. Lopez-Ortiz. A Linear Lower Boundon Index Size for Text Retrieval. In Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’01), pages 289–294.Google Scholar
  9. 9.
    P. Elias and R. A. Flower. The complexity of some simple retrieval problems. Journal of the Association for Computing Machinery, 22:367–379, 1975.MATHMathSciNetGoogle Scholar
  10. 10.
    P. Erdős and R. Rado. Intersection theorems for systems of sets. Journal of London Mathematical Society 35 (1960), pages 85–90.CrossRefGoogle Scholar
  11. 11.
    M. L. Fredman, J. Komlós, and E. Szemerédi. Storing a sparse table with O(1) worst case access time. Journal of the Association for Computing Machinery, 31:538–544, 1984.MATHMathSciNetGoogle Scholar
  12. 12.
    R. Grossi, J.S. Vitter. Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In Proc. 32th Annual ACM Symp. on Theory of Computing (STOC’00), pages 397–406.Google Scholar
  13. 13.
    R. Grossi, A. Gupta, and J.S. Vitter. High-Order Entropy-Compressed Text Indexes. In Proc. 14th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA’03), pages 841–850.Google Scholar
  14. 14.
    D. J. Kleitman and J. Spencer: Families of k-independent sets. Discrete Math. 6 (1973), pp. 255–262.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    D.E. Knuth, The Art of Computer Programming, Vol. II: Seminumerical Algorithms (Addison-Wesley, Reading, MA, 2nd ed., 1980).Google Scholar
  16. 16.
    F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier/North-Holland, Amsterdam, 1981.Google Scholar
  17. 17.
    U. Manber, S. Wu. GLIMPSE — A Tool to Search Through Entire Filesystems. White Paper. Available at http://glimpse.cs.arizona.edu/.Google Scholar
  18. 18.
    P.B. Miltersen. The bitprobe complexity measure revisited. In 10th Annual Symposium on Theoretical Aspects of Computer Science (STACS’93), pages 662–671, 1993.Google Scholar
  19. 19.
    P.B. Miltersen, On the cell probe complexity of polynomial evaluation, Theoretical Computer Science, 143:167–174, 1995.MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    P.B. Miltersen, N. Nisan, S. Safra, and A. Wigderson: On data structures and asymmetric communication complexity, Journal of Computer and System Sciences, 57:37–49, 1998.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    M. Minsky and S. Papert. Perceptrons. MIT Press, Cambridge, Mass., 1969.MATHGoogle Scholar
  22. 22.
    J. Naor and M. Naor: Small-bias probability spaces: efficient constructions and applications. SIAM J. Comput., Vol. 22, No. 4, (1993), pp. 838–856.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    M. Naor, L. Schulman, A. Srinivasan: Splitters and near optimal derandomization. In Proc. of 36th IEEE FOCS, (1995), pp. 182–191.Google Scholar
  24. 24.
    N. Nisan, S. Rudich, and M. Saks. Products and Help Bits in Decision Trees, SIAM J. Comput. 28:1035–1050, 1999.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    R. Pagh. Low redundancy in static dictionaries with O(1) lookup time. In International Colloquium on Automata Languages and Programming (ICALP’99), Lecture Notes in Computer Science, Volume 1644, pages 595–604, 1999.MathSciNetGoogle Scholar
  26. 26.
    G. Seroussi and N. Bshouty: Vector sets for exhaustive testing of logic circuits. IEEE Trans. Inform. Theory, 34 (1988), pp. 513–522.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Anna Gál
    • 1
  • Peter Bro Miltersen
    • 2
  1. 1.Dept. of Computer ScienceUniversity of Texas at AustinAustin
  2. 2.Dept. of Computer ScienceUniversity of AarhusAarhus

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