Skip to main content
Log in

Query Evaluation on a Database Given by a Random Graph

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We consider random graphs, and their extensions to random structures, with edge probabilities of the form β n α, where n is the number of vertices, α,β are fixed and α>1 (α>arity−1 for structures of higher arity). We consider conjunctive properties over these random graphs, and investigate the problem of computing their asymptotic conditional probabilities. This provides us a novel approach to dealing with uncertainty in databases, with applications to data privacy and other database problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abiteboul, S., Duschka, O.M.: Complexity of answering queries using materialized views. In: PODS, pp. 254–263 (1998)

  2. Alon, N., Spencer, J.: The Probabilistic Method. Wiley, New York (1992)

    MATH  Google Scholar 

  3. Babcock, B., Chaudhuri, S.: Towards a robust query optimizer: a principled and practical approach. In: SIGMOD, pp. 19–130 (2005)

  4. Bacchus, F., Grove, A.J., Halpern, J.Y., Koller, D.: From statistical knowledge bases to degrees of belief. Artif. Intell. 87(1–2), 75–143 (1996)

    Article  MathSciNet  Google Scholar 

  5. Bollobas, B.: Random Graphs. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  6. Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: STOC, pp. 77–90 (1977)

  7. Dalvi, N., Miklau, G., Suciu, D.: Asymptotic conditional probabilities for conjunctive queries. In: ICDT (2005)

  8. Dalvi, N., Suciu, D.: Query answering using probabilistic views. In: VLDB, pp. 805–816 (2005)

  9. Erdös, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kut. Int. Kozl. 5, 17–61 (1960)

    MATH  Google Scholar 

  10. Evfimievski, A., Gehrke, J., Srikant, R.: Limiting privacy breaches in privacy preserving data mining. In: PODS, pp. 211–222 (2003)

  11. Fagin, R.: Probabilities on finite models. J. Symb. Log. 41(1), 50–58 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fortuin, C.M., Kasteleyn, P.W., Ginibre, J.: Correlation inequalities on some partially ordered sets. Commun. Math. Phys. 22, 89–103 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  13. Getoor, L., Taskar, B., Koller, D.: Selectivity estimation using probabilistic models. In: SIGMOD, pp. 461–472 (2001)

  14. 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)

    MathSciNet  Google Scholar 

  15. Halevy, A.Y.: Answering queries using views: A survey. VLDB J. 10(4), 270–294 (2001)

    Article  MATH  Google Scholar 

  16. Hemaspaandra, L.A., Vollmer, H.: The satanic notations: Counting classes beyond #p and other definitional adventures. Technical Report, University of Rochester, Rochester, NY, USA (1994)

  17. Kifer, D., Gehrke, J.E.: Injecting utility into anonymized datasets. In: SIGMOD (2006)

  18. Lenzerini, M.: Data integration: a theoretical perspective. In: PODS, pp. 233–246 (2002)

  19. Liogon’kiĭ, M.I.: On the conditional satisfyability ratio of logical formulas. Math. Notes Acad. USSR 6, 856–861 (1969)

    Article  MathSciNet  Google Scholar 

  20. Lynch, J.F.: Probabilities of sentences about very sparse random graphs. Random Struct. Algorithms 3(l), 33–54 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lynch, J.F.: Infinitary logics and very sparse random graphs. In: Logic in Computer Science, pp. 191–198 (1993)

  22. Machanavajjhala, A., Gehrke, J., Kifer, D., Venkitasubramaniam, M.: l-diversity: Privacy beyond k-anonymity. In: ICDE, p. 24 (2006)

  23. Miklau, G., Suciu, D.: A formal analysis of information disclosure in data exchange. In: SIGMOD (2004)

  24. Spencer, J., Shelah, S.: Zero-one laws for sparse random graphs. J. Am. Math. Soc. 1, 97–115 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  25. Valiant, L.: The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  26. Vardi, M.Y.: The complexity of relational query languages. In: STOC, pp. 137–146 (1982)

  27. Wagner, K.W.: More complicated questions about maxima and minima, and some closures of NP. Theor. Comput. Sci. 51(1–2), 53–80 (1987)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nilesh Dalvi.

Additional information

This work was partially supported by the grants NSF SEIII 0513877, NSF 61-2252, and NSF IIS-0428168.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dalvi, N. Query Evaluation on a Database Given by a Random Graph. Theory Comput Syst 44, 503–532 (2009). https://doi.org/10.1007/s00224-008-9148-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-008-9148-4

Keywords

Navigation