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Acta Informatica

, Volume 44, Issue 3–4, pp 207–247 | Cite as

On the equivalence between FDs in XML and FDs in relations

  • Millist W. VincentEmail author
  • Jixue Liu
  • Mukesh Mohania
Original article

Abstract

With the growing use of the eXtensible Markup Language (XML) in database technology as a format for the permanent storage of data, the topic functional dependencies in XML (XFDs) has assumed increased importance because of its central role in database design. Recently, two different approaches have been proposed for defining an XFD. The first uses the concept of a ‘tree tuple’, whereas the second uses the concept of a ‘closest node’. In general, the two approaches are not comparable, but are comparable when a Document Type Definition is present and there is no missing information in the XML document. The first contribution of this article shows that when the two XFD definitions are comparable, the definitions are equivalent, and so there is essentially a common definition of an XFD in complete XML documents. The second contribution is to provide justification for the definition of a ‘closest node’ XFD. We show that if a complete flat relation is mapped to an XML document by an arbitrary sequence of nest operations, the XML document satisfies a ‘closest node’ XFD if and only if the relation satisfies the corresponding functional dependency. The class of XML documents generated in this fashion is a subset of the class of XML documents for which the two definitions of XFDs coincide. Hence ‘tree tuple’ and ‘closest node’ XFDs both capture the semantics of FDs when a complete relation is mapped to an XML document via arbitrary nesting.

Keywords

Inductive Hypothesis Close Property Atomic Attribute Close Node Nest Operator 
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.

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References

  1. 1.
    Abiteboul S., Hull R. and Vianu V. (1996). Foundations of databases. Addison–Wesley, Reading Google Scholar
  2. 2.
    Arenas, M., Barcelo, P., Fagin, R., Libkin, L.: Locally consistent transformations and query answering in data exchange. In: PODS, pp. 229–240 (2004)Google Scholar
  3. 3.
    Arenas, M., Libkin, L.: A normal form for XML documents. In: PODS, pp. 85–96 (2002)Google Scholar
  4. 4.
    Arenas, M., Libkin, L.: An information-theoretic approach to normal forms for relational and XML data. In: ACM Principles of Databases Conference, pp. 15–26 (2003)Google Scholar
  5. 5.
    Arenas M. and Libkin L. (2004). A normal form for XML documents. TODS 29(1): 195–232 CrossRefGoogle Scholar
  6. 6.
    Arenas M. and Libkin L. (2005). An information-theoretic approach to normal forms for relational and XML data. JACM 52(2): 246–283 CrossRefMathSciNetGoogle Scholar
  7. 7.
    Atzeni P. and DeAntonellis V. (1993). Relational Database Theory. Benjamin Cummings, Reading zbMATHGoogle Scholar
  8. 8.
    Beyer, K., Cochrane, R., Josifovski, V., Kleewein, J., Lapis, G., Lohman, G.: System RX: one part relational, one part XML. In: ACM SIGMOD Conference, pp. 347–358 (2005)Google Scholar
  9. 9.
    Boag, S., Chamberlin, D., Fernandez, M.F., Florescu, D., Robie, J., Simeon, J.: XQuery 1.0: an XML query language (2005). http://www.w3.org/TR/2005/CR-xquery-20051103/Google Scholar
  10. 10.
    Bray, T., Paoli, J., Sperberg-McQueen, C.: Extensible markup language (XML) 1.0. Technical report (1998). http://www.w3.org/Tr/1998/REC-XML-19980819Google Scholar
  11. 11.
    Buneman P., Davidson S., Fan W., Hara C. and Tan W. (2003). Reasoning about keys for XML. Inf. Syst. 28(8): 1037–1063 CrossRefGoogle Scholar
  12. 12.
    Buneman, P., Fan, W., Weinstein, S.: Path constraints on structured and semistructured data. In: ACM PODS Conference, pp. 129–138 (1998)Google Scholar
  13. 13.
    Chen, Y., Davidson, S., Hara, C., Y.Zheng: RRXS:redundancy reducing XML storage in relations. In: VLDB, pp. 189–200 (2003)Google Scholar
  14. 14.
    Cover T. and Thomas J. (1991). Elements of Information Theory. Wiley, New York zbMATHGoogle Scholar
  15. 15.
    Davidson, S., Fan, W., Hara, C., , Qin, J.: Propagating XML constraints to relations. In: The 19th International Conference on Data Engineering (ICDE), pp. 543–554 (2003)Google Scholar
  16. 16.
    Embley, D.W., Mok, W.Y.: Developing XML documents with guaranteed “good” properties. In: ER 2001, 20th International Conference on Conceptual Modeling, pp. 426 –441 (2001)Google Scholar
  17. 17.
    Fagin, R.: Normal forms and relational database operators. In: ACM SIGMOD Conference, pp. 123–134 (1979)Google Scholar
  18. 18.
    Fagin, R., Kolaitis, P., Popa, L., Tan, W.: Composing schema mappings: second-order dependencies to the rescue. In: ACM PODS Conference, pp. 83–94 (2004)Google Scholar
  19. 19.
    Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: Semantics and query answering. In: International Conference on Database Theory, pp. 207–224 (2003)Google Scholar
  20. 20.
    Fagin, R., Kolaitis, P.G., Popa, L.: Data exchange: getting to the core. In: ACM PODS conference, pp. 90–101 (2003)Google Scholar
  21. 21.
    Fan, W.: XML constraints: Specification, analysis, and applications. In: DEXA Workshops 2005, pp. 805–809 (2005)Google Scholar
  22. 22.
    Fan W. and Libkin L. (2002). On XML integrity constraints in the presence of DTDs. JACM 49(3): 368–406 CrossRefMathSciNetGoogle Scholar
  23. 23.
    Fan W. and Simeon J. (2003). Integrity constraints for XML. J. Comput. Syst. Sci. 66(1): 254–291 zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Gottlob, G., Schrefl, M., Stumptner, M.: On the interaction between transitive closure and functional dependencies. In: Second Symposium on Mathematical Fundamentals of Database Systems, pp. 187–206 (1989)Google Scholar
  25. 25.
    Halverson, A., Josifovski, V., Lohman, G., Pirahesh, H., Mšrschel, M.: ROX: Relational over XML. In: VLDB Conference, pp. 264–275 (2005)Google Scholar
  26. 26.
    Hartmann, S., T.T.: Axiomatising functional dependencies for XML with frequencies. In: FOIKS, pp. 159–178 (2006)Google Scholar
  27. 27.
    Hartmann S., Link S. and Schewe K.D. (2005). Functional dependencies over XML documents with DTDs. Acta Cybern. 17(1): 153–171 zbMATHMathSciNetGoogle Scholar
  28. 28.
    Klarlund, N., Schwentick, T., Suciu, D.: XML: Model, schemas, types, logics, and queries. In: Logics for Emerging Applications of Databases, pp. 1–41 (2003)Google Scholar
  29. 29.
    Kolahi, S.: Dependency-preserving normalization of relational and XML data. In: DBPL, pp. 247–261 (2005)Google Scholar
  30. 30.
    Lee, M., Ling, T., Low, W.L.: Designing functional dependencies for XML. In: EDBT Conference, pp. 124–141 (2002)Google Scholar
  31. 31.
    Lenzerini, M.: Data integration: a theoretical perspective. In: ACM PODS Conference, pp. 233–246 (2002)Google Scholar
  32. 32.
    Levene M. and Vincent M.W. (2000). Justification for inclusion dependency normal form. IEEE Trans. Knowl. Data Eng. 12: 281–291 CrossRefGoogle Scholar
  33. 33.
    Libkin S. (2004). Elements of Finite Model Theory. Springer, Heidelberg zbMATHGoogle Scholar
  34. 34.
    Lin T.W., Lee M.M. and Dobbie G. (2004). Semistructured Database Design. Springer, Heidelberg Google Scholar
  35. 35.
    Miller R.J., Hernndez M.A., Haas L.M., Yan L., Ho C.T.H., Fagin R. and Popa L. (2001). The clio project: Managing heterogeneity. SIGMOD Rec. 30(1): 78–83 CrossRefGoogle Scholar
  36. 36.
    Moller, A., Schwartzbach, M.: Introduction to XML and Web Technologies. Addison–Wesley, Reading (2006)Google Scholar
  37. 37.
    Schewe, K.D.: Redundancy, dependencies and normal forms for XML databases. In: ADC, pp. 7–16 (2005)Google Scholar
  38. 38.
    Thomas, S., Fischer, P.: Nested relational structures. In: Kanellakis, P. (ed.) The Theory of Databases, pp. 269 –307. JAI Press, Greenwich, CT (1986)Google Scholar
  39. 39.
    Thompson, H.S., Beech, D., Maloney, M., Mendelsohn, N.: XML Schema Part 1: Structures (2001). W3C Working Draft, http://www.w3.org/Tr/1998/XMLschema-1Google Scholar
  40. 40.
    Velegrakis, Y., Miller, R.J., Mylopoulos, J.: Representing and querying data transformations. In: Proceedings of IEEE International Conference on Data Engineering, pp. 81–92 (2005)Google Scholar
  41. 41.
    Vincent, M., Liu, J.: Multivalued dependencies and a 4NF for XML. In: CAISE, pp. 14–29 (2003)Google Scholar
  42. 42.
    Vincent, M., Liu, J.: Multivalued dependencies in XML. In: BNCOD, pp. 4–18 (2003)Google Scholar
  43. 43.
    Vincent, M., Liu, J., Liu, C.: Multivalued dependencies and a redundancy free 4NF for XML. In: XML Symposium, pp. 254–266 (2003)Google Scholar
  44. 44.
    Vincent M., Liu J. and Liu C. (2004). Strong functional dependencies and their application to normal forms in XML. TODS 29(3): 445–462 CrossRefGoogle Scholar
  45. 45.
    Vincent, M.W.: A new redundancy free normal form for relational database design. In: Database Semantics, pp. 247–264 (1998)Google Scholar
  46. 46.
    Vincent M.W. (1999). Semantic foundations of 4NF in relational database design. Acta Inf. 36: 1–41 CrossRefMathSciNetGoogle Scholar
  47. 47.
    Vincent M.W. and Levene M. (2000). Restructuring partitioned normal relations without information loss. SIAM J. Comput. 39(5): 1550–1567 CrossRefMathSciNetGoogle Scholar
  48. 48.
    Wang, J., Topor, R.: Removing XML data redundancies using functional and equality-generating dependencies. In: ADC, pp. 65–74 (2005)Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Millist W. Vincent
    • 1
    Email author
  • Jixue Liu
    • 1
  • Mukesh Mohania
    • 2
  1. 1.School of Computer and Information ScienceUniversity of South AustraliaAdelaideAustralia
  2. 2.IBM Research LaboratoriesNew DelhiIndia

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