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Average Case Analysis in Database Problems

Author

Listed:
  • Oleg Seleznjev

    (Umeå University
    Moscow State University)

  • Bernhard Thalheim

    (Brandenburg University of Technology at Cottbus)

Abstract

In a variety of applications ranging from environmental and health sciences to bioinformatics, it is essential that data collected in large databases are generated stochastically. This states qualitatively new problems both for statistics and for computer science. Namely, instead of deterministic (usually worst case) analysis, the average case analysis is needed for many standard database problems. Since both stochastic and deterministic methods and notation are used it causes additional difficulties for an investigation of such problems and for an exposition of results. We consider a general class of probabilistic models for databases and study a few problems in a probabilistic framework. In order to demonstrate the general approach, the problems for systems of database constraints (keys, functional dependencies and related) are investigated in more detail. Our approach is based on consequent using Rényi entropy as a main characteristic of uncertainty of distribution and Poisson approximation (Stein–Chen technique) of the corresponding probabilities.

Suggested Citation

  • Oleg Seleznjev & Bernhard Thalheim, 2003. "Average Case Analysis in Database Problems," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 395-418, December.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:4:d:10.1023_a:1026258911996
    DOI: 10.1023/A:1026258911996
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    References listed on IDEAS

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    1. Janson, Svante, 1987. "Poisson convergence and poisson processes with applications to random graphs," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 1-30.
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    Cited by:

    1. Leonenko, Nikolaj & Seleznjev, Oleg, 2010. "Statistical inference for the [epsilon]-entropy and the quadratic Rényi entropy," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1981-1994, October.
    2. Oleg Seleznjev & Bernhard Thalheim, 2010. "Random Databases with Approximate Record Matching," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 63-89, March.

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