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Equivalence of queries that are sensitive to multiplicities

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Abstract

The query equivalence problem has been studied extensively for set-semantics and, more recently, for bag and bag-set semantics. However, SQL queries often combine set, bag and bag-set semantics. For example, an SQL query that returns a multiset of elements may call a subquery or view that returns a set of elements. Queries may access both relations that do not contain duplicates, as well as relations with duplicates. As another example, in SQL one can compute a multiset-union of queries, each of which returns a set of answers. This paper presents combined semantics, which formally models query evaluation combining set, bag and bag-set semantics. The equivalence problem for queries evaluated under combined semantics is studied. A sufficient condition for equivalence is presented. For several important common classes of queries necessary and sufficient conditions for equivalence are presented.

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References

  1. Aho A.V., Sagiv Y., Ullman J.D.: Efficient optimization of a class of relational expressions. ACM Trans. Database Syst. 4(4), 435–454 (1979)

    Article  Google Scholar 

  2. Calvanese, D., Giacomo, G.D., Vardi, M.Y.: Decidable containment of recursive queries. In: Calvanese, D., et al. (eds.) In: Proceedings of the 9th International Conference on Database Theory, Siena, Italy, January 8–10, 2003, pp. 327–342

  3. Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: STOC, pp. 77–90. ACM Press, New York (1977)

  4. Chaudhuri, S.: An overview of query optimization in relational systems. In: PODS, pp. 34–43. ACM Press, New York (1998)

  5. Chaudhuri, S., Vardi, M.Y.: Optimization of real conjunctive queries. In: PODS, pp. 59–70. ACM Press, New York (1993)

  6. Chekuri C., Rajaraman A.: Conjunctive query containment revisited. Theor. Comput. Sci. 239(2), 211–229 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cohen, S.: Equivalence of queries combining set and bag-set semantics. In: Vansummeren, S. (ed.) Proceedings of the Twenty- Fifth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 26–28, 2006, Chicago, Illinois, Maryland, USA, pp. 70–79

  8. Cohen, S., Nutt, W., Serebrenik, A.: Rewriting aggregate queries using views. In: PODS, pp. 155–166. ACM Press, New York (1999)

  9. Cohen, S., Nutt, W., Sagiv, Y.: Containment of Aggregate Queries. In: Calvanese, D., et al. (eds.) Proceedings of the 9th International Conference on Database Theory, Siena, Italy, January 8--10, 2003, pp. 111–125

  10. Cohen S., Sagiv Y., Nutt W.: Equivalences among aggregate queries with negation. ACM Trans. Comput. Log. 6(2), 328–360 (2005)

    Article  MathSciNet  Google Scholar 

  11. Cohen, S., Nutt, W., Sagiv, Y.: Deciding equivalences among conjunctive aggregate queries. J. ACM 54(2), (2007)

  12. Dayal, U.: Of nests and trees: a unified approach to processing queries that contain nested subqueries, aggregates, and quantifiers. In: Stocker, P.M., Kent, W., Hammersley, P. (eds.) VLDB, pp. 197–208. Morgan Kaufmann, San Francisco (1987)

  13. Halevy A.Y.: Answering queries using views: a survey. VLDB J. 10(4), 270–294 (2001)

    Article  MATH  Google Scholar 

  14. Halevy A.Y., Mumick I.S., Sagiv Y., Shmueli O.: Static analysis in datalog extensions. J. ACM 48(5), 971–1012 (2001)

    Article  MathSciNet  Google Scholar 

  15. Ioannidis Y.E., Ramakrishnan R.: Containment of conjunctive queries: beyond relations as sets. ACM Trans. Database Syst. 20(3), 288–324 (1995)

    Article  Google Scholar 

  16. Jayram, T.S., Kolaitis, P.G., Vee, E.: The containment problem for real conjunctive queries with inequalities. In: Vansummeren, S. (ed.) Proceedings of the Twenty-Fifth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 26–28, 2006, Chicago, Illinois, Maryland, USA, pp. 80–89

  17. Johnson D.S., Klug A.C.: Optimizing conjunctive queries that contain untyped variables. SIAM J. Comput. 12(4), 616–640 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  18. Khizder V.L., Toman D., Weddell G.E.: Reasoning about duplicate elimination with description logic. In: Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Palamidessi, C., Pereira, L.M., Sagiv, Y., Stuckey, P.J. (eds.) Computational Logic. Lecture Notes in Computer Science, vol. 1861, pp. 1017–1032. Springer, Berlin (2000)

    Google Scholar 

  19. Kim W.: On optimizing an SQL-like nested query. ACM Trans. Database Syst. 7(3), 443–469 (1982)

    Article  MATH  Google Scholar 

  20. Klug A.C.: On conjunctive queries containing inequalities. J. ACM 35(1), 146–160 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  21. Levy, A.C., Sagiv, Y.: Semantic query optimization in datalog programs. In: PODS, pp. 163–173. ACM Press, New York (1995)

  22. Muralikrishna M.: Improved unnesting algorithms for join aggregate sql queries. In: Yuan, L.-Y. (ed) VLDB, pp. 91–102. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  23. Paulley, G.N., Larson, P.-Å.: Exploiting uniqueness in query optimization. In: ICDE, pp. 68–79. IEEE Computer Society, USA (1994)

  24. Pottinger R., Halevy A.Y.: Minicon: a scalable algorithm for answering queries using views. VLDB J. 10(2–3), 182–198 (2001)

    MATH  Google Scholar 

  25. Sagiv Y., Saraiya Y.P.: Minimizing restricted-fanout queries. Discrete Appl. Math. 40(2), 245–264 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  26. Sagiv Y., Yannakakis M.: Equivalences among relational expressions with the union and difference operators. J. ACM 27(4), 633–655 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ullman J.D.: Principles of Database and Knowledge-Base Systems, vol. I. Computer Science Press, New York (1988)

    Google Scholar 

  28. Ullman J.D.: Principles of Database and Knowledge-Base Systems, vol. II. Computer Science Press, New York (1989)

    Google Scholar 

  29. van der Meyden R.: The complexity of querying indefinite data about linearly ordered domains. J. Comput. Syst. Sci. 54(1), 113–135 (1997)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. The Selim and Rachel Benin School of Engineering and Computer Science, The Hebrew University of Jerusalem, Edmund J. Safra Campus, 91094, Jerusalem, Israel

    Sara Cohen

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  1. Sara Cohen
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Correspondence to Sara Cohen.

Additional information

An early version of this article appeared in [7]. This paper extends [7] to include bag semantics, in addition to set and bag-set semantics. This work was partially supported by the Israel Science Foundation (Grant 1032/05).

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Cohen, S. Equivalence of queries that are sensitive to multiplicities. The VLDB Journal 18, 765–785 (2009). https://doi.org/10.1007/s00778-008-0122-1

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  • DOI: https://doi.org/10.1007/s00778-008-0122-1

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