The Finite Implication Problem for Expressive XML Keys: Foundations, Applications, and Performance Evaluation

  • Flavio Ferrarotti
  • Sven Hartmann
  • Sebastian Link
  • Mauricio Marin
  • Emir Muñoz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8220)


The increasing popularity of XML for persistent data storage, processing and exchange has triggered the demand for efficient algorithms to manage XML data. Both industry and academia have long since recognized the importance of keys in XML data management. In this paper we make a theoretical as well as a practical contribution to this area. This endeavour is ambitious given the multitude of intractability results that have been established. Our theoretical contribution is based in the definition of a new fragment of XML keys that keeps the right balance between expressiveness and efficiency of maintenance. More precisely, we characterize the associated implication problem axiomatically and develop a low-degree polynomial time decision algorithm. In comparison to previous work, this new fragment of XML keys provides designers with an enhanced ability to capture properties of XML data that are significant for the application at hand. Our practical contribution includes an efficient implementation of this decision algorithm and a thorough evaluation of its performance, demonstrating that reasoning about expressive notions of XML keys can be done efficiently in practice, and scales well. Our results promote the use of XML keys on real-world XML practice, where a little more semantics makes applications a lot more effective. To exemplify this potential, we use the decision algorithm to calculate non-redundant covers for sets of XML keys. In turn, this allow us to reduce significantly the time required to validate large XML documents against keys from the proposed fragment.


Decision Algorithm Adjacency List Path Expression Client Node XPath Query 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1995)Google Scholar
  2. 2.
    Aho, A., Ullman, J., Hopcroft, J.: Data structures and algorithms. Addison-Wesley (1983)Google Scholar
  3. 3.
    Apparao, V., et al.: Document object model (DOM) level 1 specification, W3C recommendation (1998),
  4. 4.
    Arenas, M., Fan, W., Libkin, L.: What’s hard about XML schema constraints? In: Hameurlain, A., Cicchetti, R., Traunmüller, R. (eds.) DEXA 2002. LNCS, vol. 2453, pp. 269–278. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Arenas, M., Libkin, L.: XML data exchange: Consistency and query answering. J. ACM 55, 7:1–7:72 (2008)Google Scholar
  6. 6.
    Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F.: Extensible markup language (XML) 1.0, 4th edn., W3C recommendation (2006),
  7. 7.
    Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.: Keys for XML. Computer Networks 39(5), 473–487 (2002)CrossRefGoogle Scholar
  8. 8.
    Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.: Reasoning about keys for XML. Inf. Syst. 28(8), 1037–1063 (2003)CrossRefGoogle Scholar
  9. 9.
    Chen, Y., Davidson, S., Zheng, Y.: Xkvalidator: a constraint validator for XML. In: CIKM 2002: Proceedings of the 2002 ACM CIKM International Conference on Information and Knowledge Management, pp. 446–452. ACM (2002)Google Scholar
  10. 10.
    Clark, J., DeRose, S.: XML path language (XPath) version 1.0, W3C recommendation (1999),
  11. 11.
    Ferrarotti, F., Hartmann, S., Link, S., Wang, J.: Promoting the semantic capability of XML keys. In: Lee, M.L., Yu, J.X., Bellahsène, Z., Unland, R. (eds.) XSym 2010. LNCS, vol. 6309, pp. 144–153. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Ferrarotti, F., Hartmann, S., Link, S., Marin, M., Muñoz, E.: Performance analysis of algorithms to reason about XML keys. In: Liddle, S.W., Schewe, K.-D., Tjoa, A.M., Zhou, X. (eds.) DEXA 2012, Part I. LNCS, vol. 7446, pp. 101–115. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. Trans. Database Syst. 30(2), 444–491 (2005)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hartmann, S., Köhler, H., Link, S., Trinh, T., Wang, J.: On the notion of an XML key. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2008. LNCS, vol. 4925, pp. 103–112. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Database Syst. 34(2) (2009)Google Scholar
  16. 16.
    Hartmann, S., Link, S.: Expressive, yet tractable XML keys. In: EDBT 2009: 12th International Conference on Extending Database Technology. ACM International Conference Proceeding Series, vol. 360, pp. 357–367. ACM (2009)Google Scholar
  17. 17.
    Jungnickel, D.: Graphs, Networks and Algorithms. Springer (1999)Google Scholar
  18. 18.
    Liu, Y., Yang, D., Tang, S., Wang, T., Gao, J.: Validating key constraints over XML document using XPath and structure checking. Future Generation Comp. Syst. 21(4), 583–595 (2005)CrossRefGoogle Scholar
  19. 19.
    Maier, D.: Minimum Covers in the Relational Database Model. J. ACM 27, 664–674 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Miklau, G., Suciu, D.: Containment and equivalence for a fragment of XPath. J. ACM 51(1), 2–45 (2004)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Stewart, D.B., Khosla, P.K.: Mechanisms for Detecting and Handling Timing Errors. Commun. ACM 40(1), 87–93 (1997)CrossRefGoogle Scholar
  22. 22.
    Suciu, D.: XML Data Repository, University of Washington (2002),
  23. 23.
    Thompson, H., Beech, D., Maloney, M., Mendelsohn, N.: XML Schema Part 1: Structures, 2nd edn., W3C Recommendation (2004),

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Flavio Ferrarotti
    • 1
  • Sven Hartmann
    • 2
  • Sebastian Link
    • 3
  • Mauricio Marin
    • 4
  • Emir Muñoz
    • 5
  1. 1.Victoria University of WellingtonNew Zealand
  2. 2.Clausthal University of TechnologyGermany
  3. 3.The University of AucklandNew Zealand
  4. 4.Yahoo! ResearchUSA
  5. 5.DERINational University of Ireland GalwayIreland

Personalised recommendations