An Equational Chase for Path-Conjunctive Queries, Constraints, Views

  • Lucian Popa
  • Val Tannen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1540)

Abstract

We consider the class of path-conjunctive queries and constraints (dependencies) defined over complex values with dictionaries. This class includes the relational conjunctive queries and embedded dependencies, as well as many interesting examples of complex value and oodb queries and integrity constraints. We show that some important classical results on containment, dependency implication, and chasing extend and generalize to this class.

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References

  1. Abi83.
    S. Abiteboul. Algebraic analogues to fundamental notions of query and dependency theory. Technical report, INRIA, 1983.Google Scholar
  2. ABU79.
    A. V. Aho, C. Beeri, and J. D. Ullman. The theory of joins in relational databases. ACM Transactions on Database Systems, 4(3):297–314 1979.CrossRefGoogle Scholar
  3. AHV95.
    Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison-Wesley, 1995.Google Scholar
  4. ALPR91.
    M. Atkinson, C. Lecluse, P. Philbrow, and P. Richard. Design issues in amap language. In Proc. of the 3rd Int’l Workshop on Database Programming Languages (DBPL91), Nafplion, Greece, August 1991.Google Scholar
  5. ASU79.
    A. V. Aho, Y. Sagiv, and J. D. Ullman. Equivalences among relational expressions. SIAM Journal of Computing, 8(2):218–246 1979.MATHCrossRefMathSciNetGoogle Scholar
  6. BBW92.
    Val Breazu-Tannen, Peter Buneman, and Limsoon Wong. Naturally embedded query languages. In J. Biskup and R. Hull, editors, LNCS 646:Proceedings of 4th International Conference on Database Theory, Berlin, Germany, October, 1992, pages 140–154. Springer-Verlag, October 1992. Available as UPenn Technical Report MS-CIS-92-47.Google Scholar
  7. Bid87.
    N. Bidoit. The verso algebra or how to answer queries with fewer joins. Journal of Computer and System Sciences 35:321–364 1987.MATHCrossRefMathSciNetGoogle Scholar
  8. BK93.
    Catriel Beeri and Yoram Kornatzky. Algebraic optimisation of object oriented query languages. Theoretical Computer Science, 116(1):59–94, August 1993.MATHCrossRefMathSciNetGoogle Scholar
  9. BNTW95.
    Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of programming with collection types. Theoretical Computer Science, 149:3–48 1995.MATHCrossRefMathSciNetGoogle Scholar
  10. BV84.
    Catriel Beeri and Moshe Y. Vardi. A proof procedure for data dependencies Journal of the ACM, 31(4):718–741, 1984.MATHCrossRefMathSciNetGoogle Scholar
  11. Cat96.
    R. G. G. Cattell, editor. The Object Database Standard: ODMG-93. Morgan Kaufmann, San Mateo, California, 1996.MATHGoogle Scholar
  12. CD92.
    Sophie Cluet and Claude Delobel. A general framework for the optimization of object oriented queries. In M. Stonebraker, editor, Proceedings ACM-SIGMOD International Conference on Management of Data, pages 383–392, San Diego, California, June 1992.Google Scholar
  13. CGL98.
    Diego Calvanese, Giuseppe De Giacomo, and Maurizio Lenzerini. On the decidability of query containment under constraints. In Proc. 17th ACM Symposium on Principles of Database Systems, pages 149–158 1998.Google Scholar
  14. CGM88.
    U.S. Chakravarthi, J. Grant, and J. Minker. Foundations of semantic query optimization for deductive databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 243–273, San Mateo, California, 1988. Morgan-Kaufmann.Google Scholar
  15. CKV90.
    Stavros S. Cosmadakis, Paris C. Kanellakis, and Moshe Y. Vardi. Polynomial-time implication problems for unary inclusion dependencies. Journal of the ACM, 37(1):15–46 1990.MATHCrossRefMathSciNetGoogle Scholar
  16. CLM81.
    A. K. Chandra, H. R. Lewis, and J. A. Makowsky. Embedded implicationaldependencies and their inference problem. In Proceedings of ACM SIGACT Symposium on the Theory of Computing, pages 342–354, 1981.Google Scholar
  17. Clu91.
    S. Cluet. Langages et Optimisation de requetes pour Systemes de Gestion deBase de donnees oriente-objet. PhD thesis, Universite de Paris-Sud, 1991.Google Scholar
  18. CM77.
    Ashok Chandra and Philip Merlin. Optimal implementation of conjunctive queries in relational data bases. In Proceedings of 9th ACM Symposium on Theory of Computing, pages 77–90, Boulder, Colorado, May 1977.Google Scholar
  19. CR97.
    C. Chekuri and A. Rajaraman. Conjunctive query containment revisited. In LNCS 1186: Database Theory-ICDT’97, Proceedings of the 6th Int’l Conference, pages 56–70, Delphi, 1997. Springer-Verlag.Google Scholar
  20. CZ96.
    M. Cherniack and S. B. Zdonik. Rule languages and internal algebrasfor rule-based optimizers. In Proceedings of the SIGMOD International Conference on Management of Data, pages 401–412, Montreal, Quebec, Canada, 1996.Google Scholar
  21. DHP97.
    S. B. Davidson, C. Hara, and L. Popa. Querying an object-orienteddatabase using CPL. In Proceedings of the 12th Brazilian Symposium on Databases, pages 137–153, 1997. Also available as technical report MS-CIS-97-07, University of Pennsylvania.Google Scholar
  22. DS96.
    Guozhu Dong and Jianwen Su. Conjunctive query containment with respect to views and constraints. Information Processing Letters, 57(2):95–102, 1996.MATHCrossRefMathSciNetGoogle Scholar
  23. dSDA94.
    C. Souza dosSantos, C. Delobel, and S. Abiteboul. Virtual schemas and bases. In Proceedings ICEDT, March 1994.Google Scholar
  24. Fag82.
    Ronald Fagin. Horn clauses and database dependencies. Journal of the ACM, 29(4):952–985, 1982.MATHCrossRefMathSciNetGoogle Scholar
  25. FM95a.
    L. Fegaras and D. Maier. An algebraic framework for physical oodb design. In Proc. of the 5th Int’l Workshop on Database Programming Languages (DBPL95), Umbria, Italy, August 1995.Google Scholar
  26. FM95b.
    Leonidas Fegaras and David Maier. Towards an effective calculus for object query languages. In Proceedings of ACM SIGMOD International Conference on Management of Data, pages 47–58, San Jose, California, May 1995.Google Scholar
  27. FRV96.
    D. Florescu, L. Rashid, and P. Valduriez. A methodology for query reformulation in cis using semantic knowledge. International Journal of Cooperative Information Systems, 5(4), 1996.Google Scholar
  28. FW98.
    W. Fan and S. Wenstein. Interaction between path and type constraints. Technical Report MS-CIS-98-16, University of Pennsylvania, 1998.Google Scholar
  29. HD98.
    Carmem Hara and Susan Davidson. Inference rules for nested functional dependencies. Technical Report MS-CIS-98-19, University of Pennsylvania, 1998.Google Scholar
  30. JK84.
    D. S. Johnson and A. Klug. Testing containment of conjunctive queries under functional and inclusion dependencies. Journal of Computer and System Sciences, 28:167–189, 1984.MATHCrossRefMathSciNetGoogle Scholar
  31. KP82.
    A. Klug and R. Price. In determining view dependencies using tableaux. ACM Transactions on Database Systems, 7:361–381, 1982.MATHCrossRefMathSciNetGoogle Scholar
  32. LMW96.
    L. Libkin, R. Machlin, and L. Wong. A query language for multidimensional arrays: Design, implementation and optimization techniques. In SIGMOD Proceedings, Int’l Conf. on Management of Data, 1996.Google Scholar
  33. LS97.
    Alon Levy and Dan Suciu. Deciding containment for queries with complex objects. In Proc. of the 16th ACM SIGMOD Symposium on Principles of Database Systems, Tucson, Arizona, May 1997.Google Scholar
  34. LSK95.
    A. Levy, D. Srivastava, and T. Kirk. Data model and query evaluation in global information systems. Journal of Intelligent Information Systems, 1995.Google Scholar
  35. LT95.
    S. K. Lellahi and V. Tannen. Enriched monads. Technical Report ??, LRI, Univ. Paris-Sud, February 1995.Google Scholar
  36. LT97.
    Kazem Lellahi and Val Tannen. A calculus for collections and aggregates. In E. Moggi and G. Rosolini, editors, LNCS 1290: Category Theory and Computer Science Proceedings of the 7th Int'l Conference, CTCS’97, pages 261–280, Santa Margherita Ligure, September 1997. Springer-Verlag.Google Scholar
  37. Mai83.
    David Maier. The Theory of Relational Databases. Computer Science Press, Rockville, Maryland, 1983.MATHGoogle Scholar
  38. MMS79.
    D. Maier, A. O. Mendelzon, and Y. Sagiv. Testing implications of data dependencies. ACM Transactions on Database Systems, 4(4):455–469 1979.CrossRefGoogle Scholar
  39. PT98.
    Lucian Popa and Val Tannen. Chase and axioms for PC queries and dependencies. Technical Report MS-CIS-98-34, University of Pennsylvania, 1998. Available online at http://www.cis.upenn.edu/~techreports/.
  40. QR95.
    X. Qian and L. Raschid. Query interoperation among object-oriented and relational databases. In Proc. ICDE, 1995.Google Scholar
  41. Sar91.
    Y. Saraiya. Subtree elimination algorithms in deductive databases. PhD thesis, Stanford University, 1991.Google Scholar
  42. SZ89a.
    G. Shaw and S. Zdonik. Object-oriented queries: equivalence and optimization. In Proceedings of International Conference on Deductive and Object-Oriented Databases, 1989.Google Scholar
  43. SZ89b.
    G. Shaw and S. Zdonik. An object-oriented query algebra. In Proc. DBPL, Salishan Lodge, Oregon, June 1989.Google Scholar
  44. Ull89.
    Jeffrey D. Ullman. Principles of Database and Knowledge-Base Systems, volume 2. Computer Science Press, 1989.Google Scholar
  45. Wie92.
    Gio Wiederhold. Mediators in the architecture of future information systems. IEEE Computer, pages 38–49, March 1992.Google Scholar
  46. YP82.
    Mihalis Yannakakis and Christos Papadimitriou. Algebraic dependencies. Journal of Computer and System Sciences, 25:2–41, 1982.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Lucian Popa
    • 1
  • Val Tannen
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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