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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. In: Conference on Very Large Data Bases (2004)
Erdös, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kut. Int. Kozl. 5, 17–61 (1960)
Fagin, R.: Probabilities on finite models. Journal of Symbolic Logic 41(1), 50–58 (1976)
Fortuin, C., Kasteleyn, P., Ginibre, J.: Correlation inequalities on some partially ordered sets. Comm. in Math. Physics 22, 89–103 (1971)
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)
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)
Halevy, A.: Answering queries using views: A survey. VLDB Journal 10(4), 270–294 (2001)
Liogon’kiĭ, M.I.: On the conditional satisfyability ratio of logical formulas. Mathematical Notes of the Academy of the USSR 6, 856–861 (1969)
Lynch, J.F.: Probabilities of sentences about very sparse random graphs. Random Struct. Algorithms 3(1), 33–54 (1992)
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)
Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal (1949)
Spencer, J., Shelah, S.: Zero-one laws for sparse random graphs. J. Amer. Math. Soc., 97–115 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dalvi, N., Miklau, G., Suciu, D. (2004). Asymptotic Conditional Probabilities for Conjunctive Queries. In: Eiter, T., Libkin, L. (eds) Database Theory - ICDT 2005. ICDT 2005. Lecture Notes in Computer Science, vol 3363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30570-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-30570-5_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24288-8
Online ISBN: 978-3-540-30570-5
eBook Packages: Computer ScienceComputer Science (R0)