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.
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References
Abiteboul, S., Duschka, O.M.: Complexity of Answering Queries Using Materialized Views. In: Proc. PODS, pp. 254–263 (1998)
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
Abiteboul, S., Kanellakis, P., Grahne, G.: On the representation and querying of sets of possible worlds. Theor. Comput. Sci. 78(1), 158–187 (1991)
Andritsos, P., Fuxman, A., Miller, R.J.: Clean answers over dirty databases: A probabilistic approach. In: Proc. ICDE (2006)
Antova, L., Koch, C., Olteanu, D.: World-set decompositions: Expressiveness and efficient algorithms. Technical Report INFOSYS-TR-2006-12, Saarland University
Antova, L., Koch, C., Olteanu, D.: \(10^{10^6}\) worlds and beyond: Efficient representation and processing of incomplete information. In: Proc. ICDE (2007)
Arenas, M., Bertossi, L.E., Chomicki, J.: Answer sets for consistent query answering in inconsistent databases. TPLP 3(4–5), 393–424 (2003)
Benjelloun, O., Sarma, A.D., Halevy, A., Widom, J.: ULDBs: Databases with uncertainty and lineage. In: Proc. VLDB (2006)
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)
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)
Bryant, R.K.: Factoring logic functions. IBM J. Res. Develop. 31(2) (1987)
Calvanese, D., Giacomo, G.D., Lenzerini, M., Rosati, R.: Logical Foundations of Peer-To-Peer Data Integration. In: PODS 2004, pp. 241–251 (2004)
Chomicki, J., Marcinkowski, J., Staworko, S.: Computing consistent query answers using conflict hypergraphs. In: Proc. CIKM, pp. 417–426 (2004)
Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. In: Proc. VLDB, pp. 864–875 (2004)
Grahne, G.: Dependency satisfaction in databases with incomplete information. In: Proc. VLDB, pp. 37–45 (1984)
Grahne, G.: The Problem of Incomplete Information in Relational Databases. LNCS, vol. 554. Springer, Heidelberg (1991)
Green, T.J., Tannen, V.: Models for Incomplete and Probabilistic Information. In: International Workshop on Incompleteness and Inconsistency in Databases (IIDB) (2006)
Imielinski, T., Lipski, W.: Incomplete information in relational databases. Journal of ACM 31, 761–791 (1984)
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Antova, L., Koch, C., Olteanu, D. (2006). World-Set Decompositions: Expressiveness and Efficient Algorithms. In: Schwentick, T., Suciu, D. (eds) Database Theory – ICDT 2007. ICDT 2007. Lecture Notes in Computer Science, vol 4353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11965893_14
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DOI: https://doi.org/10.1007/11965893_14
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