Advertisement

World-Set Decompositions: Expressiveness and Efficient Algorithms

  • Lyublena Antova
  • Christoph Koch
  • Dan Olteanu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4353)

Abstract

Uncertain information is commonplace in real-world data management scenarios. An important challenge in this context is the ability to represent large sets of possible instances (worlds) while supporting efficient storage and processing. The recent formalism of world-set decompositions (WSDs) provides a space-efficient representation for uncertain data that also supports scalable processing. WSDs are complete for finite world-sets in that they can represent any finite set of possible worlds. For possibly infinite world-sets, we show that a natural generalization of WSDs precisely captures the expressive power of c-tables. We then show that several important problems are efficiently solvable on WSDs while they are NP-hard on c-tables. Finally, we give a polynomial-time algorithm for factorizing WSDs, i.e. an efficient algorithm for minimizing such representations.

Keywords

Incomplete Information Global Condition Query Language Expressive Power Relational Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abiteboul, S., Duschka, O.M.: Complexity of Answering Queries Using Materialized Views. In: Proc. PODS, pp. 254–263 (1998)Google Scholar
  2. 2.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)MATHGoogle Scholar
  3. 3.
    Abiteboul, S., Kanellakis, P., Grahne, G.: On the representation and querying of sets of possible worlds. Theor. Comput. Sci. 78(1), 158–187 (1991)MathSciNetGoogle Scholar
  4. 4.
    Andritsos, P., Fuxman, A., Miller, R.J.: Clean answers over dirty databases: A probabilistic approach. In: Proc. ICDE (2006)Google Scholar
  5. 5.
    Antova, L., Koch, C., Olteanu, D.: World-set decompositions: Expressiveness and efficient algorithms. Technical Report INFOSYS-TR-2006-12, Saarland UniversityGoogle Scholar
  6. 6.
    Antova, L., Koch, C., Olteanu, D.: \(10^{10^6}\) worlds and beyond: Efficient representation and processing of incomplete information. In: Proc. ICDE (2007)Google Scholar
  7. 7.
    Arenas, M., Bertossi, L.E., Chomicki, J.: Answer sets for consistent query answering in inconsistent databases. TPLP 3(4–5), 393–424 (2003)MATHMathSciNetGoogle Scholar
  8. 8.
    Benjelloun, O., Sarma, A.D., Halevy, A., Widom, J.: ULDBs: Databases with uncertainty and lineage. In: Proc. VLDB (2006)Google Scholar
  9. 9.
    Bertossi, L.E., Bravo, L., Franconi, E., Lopatenko, A.: Complexity and Approximation of Fixing Numerical Attributes in Databases Under Integrity Constraints. In: Proc. DBPL, pp. 262–278 (2005)Google Scholar
  10. 10.
    Bohannon, P., Fan, W., Flaster, M., Rastogi, R.: A Cost-Based Model and Effective Heuristic for Repairing Constraints by Value Modification. In: Proc. SIGMOD (June 2005)Google Scholar
  11. 11.
    Bryant, R.K.: Factoring logic functions. IBM J. Res. Develop. 31(2) (1987)Google Scholar
  12. 12.
    Calvanese, D., Giacomo, G.D., Lenzerini, M., Rosati, R.: Logical Foundations of Peer-To-Peer Data Integration. In: PODS 2004, pp. 241–251 (2004)Google Scholar
  13. 13.
    Chomicki, J., Marcinkowski, J., Staworko, S.: Computing consistent query answers using conflict hypergraphs. In: Proc. CIKM, pp. 417–426 (2004)Google Scholar
  14. 14.
    Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. In: Proc. VLDB, pp. 864–875 (2004)Google Scholar
  15. 15.
    Grahne, G.: Dependency satisfaction in databases with incomplete information. In: Proc. VLDB, pp. 37–45 (1984)Google Scholar
  16. 16.
    Grahne, G.: The Problem of Incomplete Information in Relational Databases. LNCS, vol. 554. Springer, Heidelberg (1991)MATHGoogle Scholar
  17. 17.
    Green, T.J., Tannen, V.: Models for Incomplete and Probabilistic Information. In: International Workshop on Incompleteness and Inconsistency in Databases (IIDB) (2006)Google Scholar
  18. 18.
    Imielinski, T., Lipski, W.: Incomplete information in relational databases. Journal of ACM 31, 761–791 (1984)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lyublena Antova
    • 1
  • Christoph Koch
    • 1
  • Dan Olteanu
    • 1
  1. 1.Lehrstuhl für InformationssystemeUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations