Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Parameterized Complexity of Queries

  • Christoph KochEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1244


Parameterized complexity theory is the study of the interaction between the fixing of parameters of input problems and their computational complexity. A central parameterized complexity concept is that of a fixed-parameter tractable (FPT) problem, which captures a strong notion of well-behavedness of a problem under the assumption that parameter values do not grow with input sizes. There is also a solid theory of fixed-parameter intractability, which gives strong evidence that for certain parameterizations of problems, no FPT algorithms can be found.

Historical Background

Fixed-parameter complexity theory is strongly associated with R. Downey and M. Fellows, who did much seminal work in the area (cf. [3, 5]). The first fixed-parameter complexity result in the context of database query evaluation was the linear-time query processing algorithm for acyclic conjunctive queries by Yannakakis in 1981 [12], which preceded the development of parameterized complexity theory (cf....

This is a preview of subscription content, log in to check access.


  1. 1.
    Benedikt M, Koch C. XPath Leashed. ACM Comput Surv. 2008;4(1):1.CrossRefGoogle Scholar
  2. 2.
    Courcelle B. Graph rewriting: an algebraic and logic approach. In: van Leeuwen J, editor. Handbook of theoretical computer science, vol. 2. Amsterdam: Elsevier B.V.; 1990. p. 193–242 .chap. 5zbMATHGoogle Scholar
  3. 3.
    Downey RG, Fellows MR. Parameterized complexity. Berlin: Springer; 1999.zbMATHCrossRefGoogle Scholar
  4. 4.
    Downey RG, Fellows MR, Taylor U. The parameterized complexity of relational database queries and an improved characterization of W[1]. In: Proceedings of the First Conference of the Centre for Discrete Mathematics and Theoretical Computer Science Combinatorics, Complexity, and Logic; 1996. p. 194–213.Google Scholar
  5. 5.
    Flum J, Grohe M. Parameterized complexity theory. Berlin: Springer; 2006.zbMATHGoogle Scholar
  6. 6.
    Frick M, Grohe M. The complexity of first-order and monadic second-order logic revisited. In: Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science; 2002. p. 215–24.Google Scholar
  7. 7.
    Gottlob G, Leone N, Scarcello F. Hypertree decompositions and tractable queries. J Comput Syst Sci. 2002;64(3):579–627.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Grohe M. Parameterized complexity for the database theorist. ACM SIGMOD Rec. 2002;31(4):86.CrossRefGoogle Scholar
  9. 9.
    Papadimitriou CH, Yannakakis M. On the complexity of database queries. In: Proceedings of the 16th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems; 1997.Google Scholar
  10. 10.
    Thatcher J, Wright J. Generalized finite automata theory with an application to a decision problem of second-order logic. Math Syst Theory. 1968;2(1):57–81.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Vardi MY. The complexity of relational query languages. In: Proceedings of the 14th Annual ACM Symposium on Theory of Computing; 1982. p. 137–46.Google Scholar
  12. 12.
    Yannakakis M. Algorithms for acyclic database schemes. In: Proceedings of the 7th International Conference on Very Data Bases; 1981. p. 82–94.Google Scholar
  13. 13.
    Yannakakis M. Perspectives on database theory. In: Proceedings of the 36th IEEE Symposium on Foundations of Computer Science; 1995. p. 224–46.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Cornell University, IthacaNew YorkUSA
  2. 2.EPFLLausanneSwitzerland

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK