Consistency of Injective Tree Patterns

Authors Claire David, Nadime Francis, Filip Murlak

Thumbnail PDF


  • Filesize: 494 kB
  • 12 pages

Document Identifiers

Author Details

Claire David
Nadime Francis
Filip Murlak

Cite AsGet BibTex

Claire David, Nadime Francis, and Filip Murlak. Consistency of Injective Tree Patterns. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 279-290, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


Testing if an incomplete description of an XML document is consistent, that is, if it describes a real document conforming to the imposed schema, amounts to deciding if a given tree pattern can be matched injectively into a tree accepted by a fixed automaton. This problem can be solved in polynomial time for patterns that use the child relation and the sibling order, but do not use the descendant relation. For general patterns the problem is in NP, but no lower bound has been known so far. We show that the problem is NP-complete already for patterns using only child and descendant relations. The source of hardness turns out to be the interplay between these relations: for patterns using only descendant we give a polynomial algorithm. We also show that the algorithm can be adapted to patterns using descendant and following-sibling, but combining descendant and next-sibling leads to intractability.
  • XML
  • incomplete information
  • injective tree patterns
  • consistency


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Serge Abiteboul, Peter Buneman, and Dan Suciu. Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann, 1999. Google Scholar
  2. Pablo Barceló, Leonid Libkin, Antonella Poggi, and Cristina Sirangelo. XML with incomplete information. J. ACM, 58(1):4, 2010. Google Scholar
  3. Michael Benedikt, Wenfei Fan, and Floris Geerts. XPath satisfiability in the presence of DTDs. J. ACM, 55(2), 2008. Google Scholar
  4. Diego Calvanese, Giuseppe De Giacomo, and Maurizio Lenzerini. Semi-structured data with constraints and incomplete information. In Description Logics, 1998. Google Scholar
  5. Claire David. Complexity of data tree patterns over XML documents. In MFCS, pages 278-289, 2008. Google Scholar
  6. Ronald Fagin, Phokion G. Kolaitis, Renée J. Miller, and Lucian Popa. Data exchange: semantics and query answering. Theor. Comput. Sci., 336(1):89-124, 2005. Google Scholar
  7. Gösta Grahne. The Problem of Incomplete Information in Relational Databases, volume 554 of Lecture Notes in Computer Science. Springer, 1991. Google Scholar
  8. Tomasz Imielinski and Witold Lipski Jr. Incomplete information in relational databases. J. ACM, 31(4):761-791, 1984. Google Scholar
  9. Yaron Kanza, Werner Nutt, and Yehoshua Sagiv. Querying incomplete information in semistructured data. J. Comput. Syst. Sci., 64(3):655-693, 2002. Google Scholar
  10. Eryk Kopczynski. Trees in trees: Is the incomplete information about a tree consistent? In CSL, pages 367-380, 2011. Google Scholar
  11. Maurizio Lenzerini. Data integration: A theoretical perspective. In PODS, pages 233-246, 2002. Google Scholar
  12. Maarten Marx. XPath with conditional axis relations. In EDBT, pages 477-494, 2004. Google Scholar
  13. Gerome Miklau and Dan Suciu. Containment and equivalence for a fragment of XPath. J. ACM, 51(1):2-45, 2004. Google Scholar
  14. Frank Neven and Thomas Schwentick. On the complexity of XPath containment in the presence of disjunction, DTDs, and variables. Log. Meth. Comput. Sci., 2(3), 2006. Google Scholar
  15. Peter T. Wood. Containment for XPath fragments under DTD constraints. In ICDT, pages 297-311, 2003. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail