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.
Similar content being viewed by others
References
Abiteboul, S., Duschka, O.M.: Complexity of answering queries using materialized views. In: PODS, pp. 254–263 (1998)
Alon, N., Spencer, J.: The Probabilistic Method. Wiley, New York (1992)
Babcock, B., Chaudhuri, S.: Towards a robust query optimizer: a principled and practical approach. In: SIGMOD, pp. 19–130 (2005)
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)
Bollobas, B.: Random Graphs. Cambridge University Press, Cambridge (2001)
Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: STOC, pp. 77–90 (1977)
Dalvi, N., Miklau, G., Suciu, D.: Asymptotic conditional probabilities for conjunctive queries. In: ICDT (2005)
Dalvi, N., Suciu, D.: Query answering using probabilistic views. In: VLDB, pp. 805–816 (2005)
Erdös, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kut. Int. Kozl. 5, 17–61 (1960)
Evfimievski, A., Gehrke, J., Srikant, R.: Limiting privacy breaches in privacy preserving data mining. In: PODS, pp. 211–222 (2003)
Fagin, R.: Probabilities on finite models. J. Symb. Log. 41(1), 50–58 (1976)
Fortuin, C.M., Kasteleyn, P.W., Ginibre, J.: Correlation inequalities on some partially ordered sets. Commun. Math. Phys. 22, 89–103 (1971)
Getoor, L., Taskar, B., Koller, D.: Selectivity estimation using probabilistic models. In: SIGMOD, pp. 461–472 (2001)
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.Y.: Answering queries using views: A survey. VLDB J. 10(4), 270–294 (2001)
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)
Kifer, D., Gehrke, J.E.: Injecting utility into anonymized datasets. In: SIGMOD (2006)
Lenzerini, M.: Data integration: a theoretical perspective. In: PODS, pp. 233–246 (2002)
Liogon’kiĭ, M.I.: On the conditional satisfyability ratio of logical formulas. Math. Notes Acad. USSR 6, 856–861 (1969)
Lynch, J.F.: Probabilities of sentences about very sparse random graphs. Random Struct. Algorithms 3(l), 33–54 (1992)
Lynch, J.F.: Infinitary logics and very sparse random graphs. In: Logic in Computer Science, pp. 191–198 (1993)
Machanavajjhala, A., Gehrke, J., Kifer, D., Venkitasubramaniam, M.: l-diversity: Privacy beyond k-anonymity. In: ICDE, p. 24 (2006)
Miklau, G., Suciu, D.: A formal analysis of information disclosure in data exchange. In: SIGMOD (2004)
Spencer, J., Shelah, S.: Zero-one laws for sparse random graphs. J. Am. Math. Soc. 1, 97–115 (1988)
Valiant, L.: The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)
Vardi, M.Y.: The complexity of relational query languages. In: STOC, pp. 137–146 (1982)
Wagner, K.W.: More complicated questions about maxima and minima, and some closures of NP. Theor. Comput. Sci. 51(1–2), 53–80 (1987)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by the grants NSF SEIII 0513877, NSF 61-2252, and NSF IIS-0428168.
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-008-9148-4