Daniel Deutch
Tova Milo
ABSTRACT
We study highly expressive query languages such as datalog, fixpoint, and while-languages on probabilistic databases. We generalize these languages such that computation steps (e.g. datalog rules) can fire probabilistically. We define two possible semantics for such query languages, namely inflationary semantics where the results of each computation step are added to the current database and noninflationary queries that induce a random walk in-between database instances. We then study the complexity of exact and approximate query evaluation under these semantics.
- S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995. Google Scholar
Digital Library
- P. Agrawal, O. Benjelloun, A. Das Sarma, C. Hayworth, S. U. Nabar, T. Sugihara, and J. Widom. "Trio: A System for Data, Uncertainty, and Lineage". In VLDB, 2006. Google ScholarDigital Library
- L. Antova, C. Koch, and D. Olteanu. "From Complete to Incomplete Information and Back". In Proc. SIGMOD, 2007. Google ScholarDigital Library
- L. Antova, C. Koch, and D. Olteanu. "Query Language Support for Incomplete Information in the MayBMS System". In Proc. VLDB, 2007. Google ScholarDigital Library
- V. Bansal. "Computational Methods for Analyzing Human Genetic Variations". PhD thesis, University of California, San Diego, 2009. Google ScholarDigital Library
- O. Benjelloun, A. D. Sarma, C. Hayworth, and J. Widom. "An Introduction to ULDBs and the Trio System". IEEE Data Engineering Bulletin, 2006.Google Scholar
- D. P. Bertsekas and J. N. Tsitsiklis. Introduction to Probability. MIT Press, 2008.Google Scholar
- N. Dalvi and D. Suciu. "Efficient query evaluation on probabilistic databases". VLDB Journal, 16(4):523--544, 2007. Google ScholarDigital Library
- L. De Raedt, A. Kimmig, and H. Toivonen. "ProbLog: A Probabilistic Prolog and Its Application in Link Discovery". In IJCAI, 2007. Google ScholarDigital Library
- D. Freedman. Markov Chains. Springer-Verlag, 1983.Google Scholar
- N. Fuhr. "Probabilistic Datalog - A Logic For Powerful Retrieval Methods". In Proc. SIGIR, pages 282--290, 1995. Google ScholarDigital Library
- M. Goetz and C. Koch. "A Compositional Framework for Complex Queries over Uncertain Data". In Proc. ICDT, 2009. Google ScholarDigital Library
- T. J. Green and V. Tannen. "Models for Incomplete and Probabilistic Information". IEEE Data Eng. Bull., 29(1):17--24, 2006.Google Scholar
- M. Jerrum and A. Sinclair. "The Markov chain Monte Carlo method: an approach to approximate counting and integration". Approximation algorithms for NP-hard problems, 1997. Google ScholarDigital Library
- C. Koch. "Approximating Predicates and Expressive Queries on Probabilistic Databases". In Proc. PODS, 2008. Google ScholarDigital Library
- C. Koch. "On Query Algebras for Probabilistic Databases". SIGMOD Record, 37(4):78--85, 2008. Google ScholarDigital Library
- C. Koch. "A Compositional Query Algebra for Second-Order Logic and Uncertain Databases". In Proc. ICDT, 2009. Google ScholarDigital Library
- C. H. Papadimitriou. Computational complexity. Addison-Wesley, 1994.Google Scholar
- D. Randall. "Mixing (a tutorial on Markov Chains)". In FOCS, 2003. Google ScholarDigital Library
- C. Re, N. Dalvi, and D. Suciu. "Efficient Top-k Query Evaluation on Probabilistic Data". In ICDE, 2007.Google ScholarCross Ref
- P. Sen and A. Deshpande. "Representing and Querying Correlated Tuples in Probabilistic Databases". In ICDE, 2007.Google ScholarCross Ref
- D. Sorensen and D. Gianola. "Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics". Springer-Verlag, New York, July 2002.Google ScholarCross Ref
- Stanford Trio Project. "TriQL - The Trio Query Language", 2006.Google Scholar
- L. Valiant. "The complexity of computing the permanent". Theoretical Computer Science, 8(2):189--201, 1979.Google ScholarCross Ref
- M. Y. Vardi. "The Complexity of Relational Query Languages". In Proc. STOC, pages 137--146, 1982. Google ScholarDigital Library
- V. V. Vazirani. Approximation Algorithms. Springer, 2004. Google ScholarDigital Library
Index Terms
- On probabilistic fixpoint and Markov chain query languages
Recommendations
Horn clauses and the fixpoint query hierarchy
PODS '82: Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systemsA logic program consists of a set of Horn clauses, and can be used to express a query on relational data bases. It is shown that logic programs express precisely the queries in YE+ (the set of queries representable by a fixpoint applied to a positive ...
Query evaluation in deductive databases with alternating fixpoint semantics
First-order formulas allow natural descriptions of queries and rules. Van Gelder's alternating fixpoint semantics extends the well-founded semantics of normal logic programs to general logic programs with arbitrary first-order formulas in rule bodies. ...
Query languages for data exchange: beyond unions of conjunctive queries
ICDT '09: Proceedings of the 12th International Conference on Database TheoryThe class of unions of conjunctive queries (UCQ) has been shown to be particularly well-behaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this ...
Comments