Asymptotic Conditional Probabilities for Conjunctive Queries

  • Nilesh Dalvi
  • Gerome Miklau
  • Dan Suciu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3363)

Abstract

We study the asymptotic probabilities of conjunctive queries on random graphs.We consider a probabilistic model where the expected graph size remains constant independent of the number of vertices. While it has been known that a convergence law holds for conjunctive queries under this model, we focus on the calculation of conditional probabilities. This has direct applications to database problems like query-view security, i.e. evaluating the probability of a sensitive query given the knowledge of a set of published views. We prove that a convergence law holds for conditional probabilities of conjunctive queries and we give a procedure for calculating the conditional probabilities.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. In: Conference on Very Large Data Bases (2004)Google Scholar
  2. 2.
    Erdös, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kut. Int. Kozl. 5, 17–61 (1960)MATHGoogle Scholar
  3. 3.
    Fagin, R.: Probabilities on finite models. Journal of Symbolic Logic 41(1), 50–58 (1976)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fortuin, C., Kasteleyn, P., Ginibre, J.: Correlation inequalities on some partially ordered sets. Comm. in Math. Physics 22, 89–103 (1971)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fuhr, N., Ršlleke, T.: A probabilistic relational algebra for the integration of information retrieval and database systems. ACM Transactions on Information Sysytems 15(1), 32–66 (1997)CrossRefGoogle Scholar
  6. 6.
    Glebskiĭ, Y.V., Kogan, D.I., Liogon’kiĭ, M.I., Talanov, V.A.: Range and degree of realizability of formulas in the restricted predicate calculus. Kibernetika 2, 17–28 (1969); Engl. Transl. Cybernetics 5, 142–154 (1972)Google Scholar
  7. 7.
    Halevy, A.: Answering queries using views: A survey. VLDB Journal 10(4), 270–294 (2001)MATHCrossRefGoogle Scholar
  8. 8.
    Liogon’kiĭ, M.I.: On the conditional satisfyability ratio of logical formulas. Mathematical Notes of the Academy of the USSR 6, 856–861 (1969)Google Scholar
  9. 9.
    Lynch, J.F.: Probabilities of sentences about very sparse random graphs. Random Struct. Algorithms 3(1), 33–54 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Miklau, G., Suciu, D.: A formal analysis of information disclosure in data exchange. In: ACM SIGMOD International Conference on Management of Data, pp. 563–574 (June 2004)Google Scholar
  11. 11.
    Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal (1949)Google Scholar
  12. 12.
    Spencer, J., Shelah, S.: Zero-one laws for sparse random graphs. J. Amer. Math. Soc., 97–115 (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nilesh Dalvi
    • 1
  • Gerome Miklau
    • 1
  • Dan Suciu
    • 1
  1. 1.University of Washington 

Personalised recommendations