Abstract
We review key constraints in the context of XML as introduced by Buneman et al. We show that one of the proposed inference rules is not sound in general, and the axiomatisation proposed for XML keys is incomplete even if key paths are simple. Therefore, the axiomatisation and also the implication problem for XML keys are still unsolved.
We propose a set of inference rules that is indeed sound and complete for the implication of XML keys with simple key paths. Our completeness proof enables us to characterise the implication of XML keys in terms of the reachability problem of nodes in a digraph. This results in a quadratic time algorithm for deciding XML key implication, and shows that reasoning for XML keys is practically efficient.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
Apparao, V., et al.: Document object model (DOM) level 1 specification, W3C recommendation (October 1998), http://www.w3.org/TR/REC-DOM-Level-1/
Arenas, M., Libkin, L.: A normal form for XML documents. TODS 29(1), 195–232 (2004)
Arenas, M., Libkin, L.: An information-theoretic approach to normal forms for relational and XML data. J. ACM 52(2), 246–283 (2005)
Benedikt, M., Fan, W., Kuper, G.: Structural properties of XPath fragments. TCS 336(1), 3–31 (2005)
Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F.: Extensible markup language (XML) 1.0 (3rd edn.) W3C recommendation (February 2004) http://www.w3.org/TR/2004/REC-xml-20040204/
Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.: Reasoning about keys for XML. In: DBPL, pp. 133–148 (2001)
Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.: Keys for XML. Computer Networks 39(5), 473–487 (2002)
Buneman, P., Davidson, S., Fan, W., Hara, C., Tan, W.: Reasoning about keys for XML. Inf. Syst. 28(8), 1037–1063 (2003)
Buneman, P., Fan, W., Siméon, J., Weinstein, S.: Constraints for semi-structured data and XML. SIGMOD Record 30(1), 47–54 (2001)
Buneman, P., Fan, W., Weinstein, S.: Path constraints in semistructured databases. JCSS 61(2), 146–193 (2000)
Clark, J., DeRose, S.: XML path language (XPath) version 1.0, W3C recommendation (November 1999), http://www.w3.org/TR/xpath
Deutsch, A., Tannen, V.: Containment and integrity constraints for XPath. In: KRDB (2001)
Fagin, R., Vardi, M.Y.: The theory of data dependencies. In: ICALP, pp. 1–22 (1984)
Fan, W.: XML constraints. In: DEXA Workshops, pp. 805–809 (2005)
Fan, W., Libkin, L.: On XML integrity constraints in the presence of DTDs. J. ACM 49(3), 368–406 (2002)
Fan, W., Siméon, J.: Integrity constraints for XML. JCSS 66(1), 254–291 (2003)
Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. TODS 30(2), 444–491 (2005)
Hara, C., Davidson, S.: Reasoning about nested functional dependencies. In: PODS, pp. 91–100 (1999)
Hartmann, S., Link, S.: More functional dependencies for XML. In: Kalinichenko, L.A., Manthey, R., Thalheim, B., Wloka, U. (eds.) ADBIS 2003. LNCS, vol. 2798, pp. 355–369. Springer, Heidelberg (2003)
Hartmann, S., Link, S.: Multivalued dependencies in the presence of lists. In: PODS, pp. 330–341 (2004)
Hartmann, S., Trinh, T.: Axiomatising functional dependencies for XML with frequencies. In: Dix, J., Hegner, S.J. (eds.) FoIKS 2006. LNCS, vol. 3861, pp. 159–178. Springer, Heidelberg (2006)
Jungnickel, D.: Graphs, Networks and Algorithms. Springer, Heidelberg (1999)
Kay, M.: XSL transformations (XSLT) version 2.0 W3C candidate recommendation (November 2005), http://www.w3.org/TR/xslt20/
Miklau, G., Suciu, D.: Containment and equivalence for a fragment of XPath. J. ACM 51(1), 2–45 (2004)
Neven, F., Schwentick, T.: XPath containment in the presence of disjunction, DTDs, and variables. In: ICDT, pp. 315–329 (2003)
Paredaens, J., De Bra, P., Gyssens, M., Van Gucht, D.: The Structure of the Relational Database Model. Springer, Heidelberg (1989)
Suciu, D.: On database theory and XML. SIGMOD Record 30(3), 39–45 (2001)
Thalheim, B.: Dependencies in Relational Databases, Teubner (1991)
Thompson, H., Beech, D., Maloney, M., Mendelsohn, N.: XML Schema Part 1: Structures Second Edition, W3C Recommendation (October 28, 2004), http://www.w3.org/TR/xmlschema-1/
Vianu, V.: A web odyssey: from Codd to XML. SIGMOD Record 32(2), 68–77 (2003)
Vincent, M., Liu, J., Liu, C.: Strong functional dependencies and their application to normal forms in XML. TODS 29(3), 445–462 (2004)
Widom, J.: Data management for XML: Research directions. Data Eng. Bull. 22(3), 44–52 (1999)
Wood, P.: Containment for XPath fragments under DTD constraints. In: ICDT, pp. 300–314 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hartmann, S., Link, S. (2006). Unlocking Keys for XML Trees. In: Schwentick, T., Suciu, D. (eds) Database Theory – ICDT 2007. ICDT 2007. Lecture Notes in Computer Science, vol 4353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11965893_8
Download citation
DOI: https://doi.org/10.1007/11965893_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69269-0
Online ISBN: 978-3-540-69270-6
eBook Packages: Computer ScienceComputer Science (R0)