Document Open Access Logo

Nesting Depth of Operators in Graph Database Queries: Expressiveness vs. Evaluation Complexity

Authors M. Praveen, B. Srivathsan

Thumbnail PDF


  • Filesize: 0.53 MB
  • 14 pages

Document Identifiers

Author Details

M. Praveen
B. Srivathsan

Cite AsGet BibTex

M. Praveen and B. Srivathsan. Nesting Depth of Operators in Graph Database Queries: Expressiveness vs. Evaluation Complexity. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 117:1-117:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


Designing query languages for graph structured data is an active field of research, where expressiveness and efficient algorithms for query evaluation are conflicting goals. To better handle dynamically changing data, recent work has been done on designing query languages that can compare values stored in the graph database, without hard coding the values in the query. The main idea is to allow variables in the query and bind the variables to values when evaluating the query. For query languages that bind variables only once, query evaluation is usually NP-complete. There are query languages that allow binding inside the scope of Kleene star operators, which can themselves be in the scope of bindings and so on. Uncontrolled nesting of binding and iteration within one another results in query evaluation being PSPACE-complete. We define a way to syntactically control the nesting depth of iterated bindings, and study how this affects expressiveness and efficiency of query evaluation. The result is an infinite, syntactically defined hierarchy of expressions. We prove that the corresponding language hierarchy is strict. Given an expression in the hierarchy, we prove that it is undecidable to check if there is a language equivalent expression at lower levels. We prove that evaluating a query based on an expression at level i can be done in level i of the polynomial time hierarchy. Satisfiability of quantified Boolean formulas can be reduced to query evaluation; we study the relationship between alternations in Boolean quantifiers and the depth of nesting of iterated bindings.
  • graphs with data
  • regular data path queries
  • expressiveness
  • query evaluation
  • complexity


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


  1. P. Barceló. Querying graph databases. In Proceedings of PODS, pages 175-188, New York, NY, USA, 2013. ACM. Google Scholar
  2. P. Barceló, J. Reutter, and L. Libkin. Parameterized regular expressions and their languages. Theoretical Computer Science, 474:21-45, 2013. Google Scholar
  3. Yijia Chen, J. Flum, and M. Grohe. Bounded nondeterminism and alternation in parameterized complexity theory. In Computational Complexity, 2003, pages 13-29, 2003. Google Scholar
  4. T. Colcombet and A. Manuel. Generalized data automata and fixpoint logic. In FSTTCS, volume 29 of LIPIcs, pages 267-278, 2014. Google Scholar
  5. T. Colcombet and A. Manuel. Combinatorial expressions and lower bounds. In STACS, volume 30 of LIPIcs, pages 249-261, 2015. Google Scholar
  6. T. Colcombet and A. Manuel. Fragments of fixpoint logic on data words. In FSTTCS, volume 45 of LIPIcs, pages 98-111, 2015. Google Scholar
  7. R. De Haan, M. Kronegger, and A. Pfandler. Fixed-parameter tractable reductions to sat for planning. In Proceedings of IJCAI, pages 2897-2903, 2015. Google Scholar
  8. R. G. Downey and M. R. Fellows. Fundamentals of Parameterized Complexity. Thomson Brooks/Cole, 1997. Google Scholar
  9. L. C. Eggan. Transition graphs and the star-height of regular events. Michigan Math. J., 10(4):385-397, 1963. Google Scholar
  10. O. Grumberg, O. Kupferman, and S. Sheinvald. Variable automata over infinite alphabets. In LATA, volume 6031 of LNCS, pages 561-572, 2010. Google Scholar
  11. C. Gutierrez, C. Hurtado, and A. Mendelzon. Foundations of semantic web databases. JCSS, 77(3):520-541, 2011. Google Scholar
  12. E.V. Kostylev, J.L. Reutter, and D. Vrgoč. Containment of data graph queries. In ICDT, pages 131-142, 2014. Google Scholar
  13. U. Leser. A query language for biological networks. Bioinformatics, 21(suppl 2):ii33-ii39, 2005. Google Scholar
  14. L. Libkin, W. Martens, and D. Vrgoč. Querying graph databases with xpath. In ICDT, pages 129-140, New York, NY, USA, 2013. ACM. Google Scholar
  15. L. Libkin, T. Tan, and D. Vrgoč. Regular expressions with binding over data words for querying graph databases. In DLT, volume 7907 of LNCS, pages 325-337, 2013. Google Scholar
  16. L. Libkin and D. Vrgoč. Regular path queries on graphs with data. In ICDT, pages 74-85, 2012. Google Scholar
  17. F. Neven, T. Schwentick, and V. Vianu. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Logic, 5(3):403-435, 2004. Google Scholar
  18. W3C Recommendation. Sparql 1.1 query language. 21 March 2013. Google Scholar
  19. R. Ronen and O. Shmueli. Soql: A language for querying and creating data in social networks. In ICDE, pages 1595-1602, 2009. Google Scholar
  20. L. Segoufin. Automata and logics for words and trees over an infinite alphabet. In CSL, volume 4207 of LNCS, pages 41-57, 2006. Google Scholar
  21. M. Sipser. Introduction to the Theory of Computation. Springer, 2013. Google Scholar
  22. T. Tan. Graph reachability and pebble automata over infinite alphabets. ACM Trans. Comput. Logic, 14(3):19:1-19:31, 2013. Google Scholar
  23. D. Vrgoč. Using variable automata for querying data graphs. Information Processing Letters, 115(3):425-430, 2015. 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