An XML Algebra for XQuery

  • Leonid Novak
  • Alexandre Zamulin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4152)


An XML algebra supporting the XQuery query language is presented. The usage of expression constructing operators instead of high-order operations using functions as parameters has permitted us to remain in the limits of first-order structures whose instance is a many-sorted algebra. The set of operators of the presented algebra substantially differs from the set of operators of relation algebra. It is caused by the complex nature of the XML data model comparing with relational one. Actually, only predicative selection is more or less same in both algebra. Yet, the XML algebra in addittion permits selection by node test. The relational projection operator is replaced by the path expression and navigating functions; the join operator is replaced by unnesting join expressions. In addition, a number of node constructing expressions permitting update of the algebra state are defined.


Relation Algebra Element Node Node Accessor Path Expression Document Tree 
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  1. 1.
    Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, M., Zito, J.: Two simplified algorithms for maintaining order in a list. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 152–164. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bose, S., et al.: A Query Algebra for Fragmented XML Stream Data. In: Proc. 9th Intnl. Conference on Databases and Programming Languages, Germany (September 2003)Google Scholar
  3. 3.
    Chen, Z., et al.: From Tree Patterns to Generalized Tree Patterns: On Efficient Evaluation of XQuery. In: Proc. VLDB Conf., Berlin, Germany, (September 2003)Google Scholar
  4. 4.
    Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specifications 1, Equations and Initial Semantics. EATCS Monographs on Theoretical Computer Science, vol. 6. Springer, Berlin (1985)Google Scholar
  5. 5.
    Fernández, M., Siméon, J., Wadler, P.: An Algebra for XML Query. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 11–45. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Fisher, D., Lam, F., Wong, R.K.: Algebraic Transformation and Optimization for XQuery. In: Yu, J.X., Lin, X., Lu, H., Zhang, Y. (eds.) APWeb 2004. LNCS, vol. 3007, pp. 201–210. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Jagadish, H.V., et al.: Tax: A Tree Algebra for XML. In: Proc. Intl. Workshop on Databases and Programming Languages, Marino, Italy (September 2001), pp. 149–164 (2001)Google Scholar
  8. 8.
    Jagadish, H.V., Al-Khalifa, S., Chapman, A., et al.: TIMBER: A Native XML Database. The VLDB Journal 11(4), 274–291 (2002)MATHCrossRefGoogle Scholar
  9. 9.
    Lellahi, K., Zamulin, A.V.: Object-oriented database as a dynamic system with implicit state. In: Caplinskas, A., Eder, J. (eds.) ADBIS 2001. LNCS, vol. 2151, pp. 239–252. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Novak, L., Zamulin, A.: Algebraic Semantics of XML Schema. In: Eder, J., Haav, H.-M., Kalja, A., Penjam, J. (eds.) ADBIS 2005. LNCS, vol. 3631, pp. 209–222. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Novak, L., Zamulin, A.: An XML algebra for XQuery (preliminary communication). Preprint No. 117, A.P. Ershov Institute of Informatics Systems (2004),
  12. 12.
    Papakonstantinou, Y., et al.: XML Queries and Algebra in the Enosys Integration Platform,
  13. 13.
    Paparizos, S., et al.: A Physical Algebra for XML,
  14. 14.
    Paparizos, S., et al.: Tree Logical Classes for Efficient Evaluation of XQuery. In: Proc. SIGMOD Conf., Paris, France (June 2004)Google Scholar
  15. 15.
    Sartiani, C., Albano, A.: Yet Another Query Algebra For XML Data. In: IDEAS 2002, pp. 106–115 (2002)Google Scholar
  16. 16.
    The XML Query Algebra, W3C Working Draft (February 15, 2001),
  17. 17.
    XQuery 1.0: An XML Query Language. W3C Candidate Recommendation (November 3, 2005)Google Scholar
  18. 18.
    XQuery 1.0 and XPath 2.0 Formal Semantics, W3C Candidate Recommendation (November 3, 2005)Google Scholar
  19. 19.
    XQuery 1.0 and XPath 2.0 Data Model, W3C Candidate Recommendation (November 3, 2005)Google Scholar
  20. 20.
    XQuery 1.0 and XPath 2.0 Functions and Operators. W3C Candidate Recommendation (November 3, 2005)Google Scholar
  21. 21.
    Zhang, X., Rundensteiner, E.: XAT: XML Algebra for Rainbow System. Worcester Polytechnic Institute, Technical Report WPI-CS-TR-02-24 (July 2002)Google Scholar
  22. 22.
    Zhang, M., Yao, J.T.: XML Algebra for Data Mining. In: Proc. of SPIE, Data Mining and Knowledge Discovery: Theory, Tools, and Technology VI, Orlando, USA, April 12-13, 2004, vol. 5433, pp. 209–217 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Leonid Novak
    • 1
  • Alexandre Zamulin
    • 2
  1. 1.Institute of System ProgrammingRussian Academy of SciencesMoscowRussia
  2. 2.A.P. Ershov Institute of Informatics SystemsSiberian Branch of Russian Academy of SciencesNovosibirskRussia

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