Validity of Tree Pattern Queries with Respect to Schema Information

  • Henrik Björklund
  • Wim Martens
  • Thomas Schwentick
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)

Abstract

We prove that various containment and validity problems for tree pattern queries with respect to a schema are EXPTIME-complete. When one does not require the root of a tree pattern query to match the root of a tree, validity of a non-branching tree pattern query with respect to a Relax NG schema or W3C XML Schema is already EXPTIME-hard when the query does not branch and uses only child axes. These hardness results already hold when the alphabet size is fixed. Validity with respect to a DTD is proved to be EXPTIME-hard already when the query only uses child axes and is allowed to branch only once.

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References

  1. 1.
    Arenas, M., Daenen, J., Neven, F., Van den Bussche, J., Ugarte, M., Vansummeren, S.: Discovering XSD keys from XML data. In: SIGMOD (to appear, 2013)Google Scholar
  2. 2.
    Benedikt, M., Bourhis, P., Senellart, P.: Monadic datalog containment. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 79–91. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Benedikt, M., Fan, W., Geerts, F.: XPath satisfiability in the presence of DTDs. J. ACM 55(2) (2007)Google Scholar
  4. 4.
    Björklund, H., Gelade, W., Martens, W.: Incremental XPath evaluation. ACM Trans. Database Syst. 35(4), 29 (2010)CrossRefGoogle Scholar
  5. 5.
    Björklund, H., Martens, W., Schwentick, T.: Optimizing conjunctive queries over trees using schema information. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 132–143. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F.: Extensible Markup Language XML 1.0 (5th edn.). World Wide Web Consortium (2008)Google Scholar
  7. 7.
    Chlebus, B.S.: Domino-tiling games. JCSS 32(3), 374–392 (1986)MathSciNetMATHGoogle Scholar
  8. 8.
    Clark, J., DeRose, S.: XML Path Language (XPath) version 1.0. Technical report, World Wide Web Consortium (1999), http://www.w3.org/TR/xpath/
  9. 9.
    Clark, J., Murata, M.: Relax NG specification (2001), http://www.relaxng.org
  10. 10.
    Flesca, S., Furfaro, F., Masciari, E.: On the minimization of XPath queries. J. ACM 55(1) (2008)Google Scholar
  11. 11.
    Gelade, W., Idziaszek, T., Martens, W., Neven, F.: Simplifying XML Schema: Single-type approximations of regular tree languages. In: PODS (2010)Google Scholar
  12. 12.
    Hashimoto, K., Kusunoki, Y., Ishihara, Y., Fujiwara, T.: Validity of positive XPath queries with wildcard in the presence of DTDs. In: DBPL (2011)Google Scholar
  13. 13.
    Martens, W., Neven, F., Schwentick, T.: Simple off the shelf abstractions for XML Schema. SIGMOD Record 36(3), 15–22 (2007)CrossRefGoogle Scholar
  14. 14.
    Martens, W., Neven, F., Schwentick, T., Bex, G.J.: Expressiveness and complexity of XML Schema. ACM Trans. Database Syst. 31(3), 770–813 (2006)CrossRefGoogle Scholar
  15. 15.
    Miklau, G., Suciu, D.: Containment and equivalence for a fragment of XPath. J. ACM 51(1), 2–45 (2004)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Murlak, F., Ogiński, M., Przybyłko, M.: Between tree patterns and conjunctive queries: Is there tractability beyond acyclicity? In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 705–717. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Neven, F., Schwentick, T.: On the complexity of XPath containment in the presence of disjunction, DTDs, and variables. LMCS 2(3) (2006)Google Scholar
  18. 18.
    Stockmeyer, L., Meyer, A.: Word problems requiring exponential time: Preliminary report. In: STOC, pp. 1–9 (1973)Google Scholar
  19. 19.
    Thompson, H.S., Mendelsohn, N., Beech, D., Maloney, M.: XML Schema Definition Language (XSD) 1.1, http://www.w3.org/TR/xmlschema11-1/

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Henrik Björklund
    • 1
  • Wim Martens
    • 2
  • Thomas Schwentick
    • 3
  1. 1.Umeå UniversitySweden
  2. 2.University of BayreuthGermany
  3. 3.TU Dortmund UniversityGermany

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