iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/11821069_5
The Structure of Tractable Constraint Satisfaction Problems | SpringerLink
Skip to main content

The Structure of Tractable Constraint Satisfaction Problems

  • Conference paper
Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

  • 1077 Accesses

Abstract

We give a survey of recent results on the complexity of constraint satisfaction problems. Our main emphasis is on tractable structural restrictions.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Adler, I., Gottlob, G., Grohe, M.: Hypertree-width and related hypergraph invariants. In: Felsner, S. (ed.) Proceedings of the 3rd European Conference on Combinatorics, Graph Theory, and Applications. DMTCS Proceedings Series, vol. AE, pp. 5–10 (2005)

    Google Scholar 

  2. Arnborg, S., Corneil, D., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic Discrete Methods 8, 277–284 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bulatov, A.: Tractable conservative constraint satisfaction problems. In: Proceedings of the 18th IEEE Symposium on Logic in Computer Science, pp. 321–330 (2003)

    Google Scholar 

  5. Bulatov, A.: H-coloring dichotomy revisited. Theoretical Computer Science 349, 31–39 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bulatov, A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. Journal of the ACM 53, 66–120 (2006)

    Article  MathSciNet  Google Scholar 

  7. Bulatov, A., Krokhin, A., Jeavons, P.: The complexity of maximal constraint languages. In: Proceedings of the 33rd ACM Symposium on Theory of Computing, pp. 667–674 (2001)

    Google Scholar 

  8. Bulatov, A., Krokhin, A., Jeavons, P.: Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing 34, 720–742 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, H., Dalmau, V.: Beyond hypertree width: Decomposition methods without decompositions. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 167–181. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Chen, H., Grohe, M.: Constraint satisfaction with succinctly specified relations (in preparation)

    Google Scholar 

  11. Cohen, D., Jeavons, P.: The complexity of constraint languages. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 6. Elsevier, Amsterdam (2006)

    Google Scholar 

  12. Cohen, D., Jeavons, P., Gyssens, M.: A unified theory of structural tractability for constraint satisfaction and spread cut decomposition. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (2005) (to appear)

    Google Scholar 

  13. Dalmau, V.: Generalized majority-minority operations are tractable. In: Proceedings of the 20th IEEE Symposium on Logic in Computer Science, pp. 438–447 (2005)

    Google Scholar 

  14. Dalmau, V., Kolaitis, P.G., Vardi, M.Y.: Constraint satisfaction, bounded treewidth, and finite-variable logics. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 310–326. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  16. Feder, T., Vardi, M.Y.: The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM Journal on Computing 28, 57–104 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)

    Google Scholar 

  18. Freuder, E.C.: Complexity of k-tree structured constraint satisfaction problems. In: Proceedings of the 8th National Conference on Artificial Intelligence, pp. 4–9 (1990)

    Google Scholar 

  19. Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. Journal of Computer and System Sciences 64, 579–627 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Grohe, M.: The complexity of homomorphism and constraint satisfaction problems seen from the other side. In: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, pp. 552–561 (2003)

    Google Scholar 

  21. Grohe, M., Marx, D.: Constraint solving via fractional edge covers. In: Proceedings of the of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 289–298 (2006)

    Google Scholar 

  22. Hell, P., Nešetřil, J.: On the complexity of H-coloring. Journal of Combinatorial Theory, Series B 48, 92–110 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  23. Hell, P., Nešetřil, J., Zhu, X.: Complexity of tree homomorphisms. Discrete Applied Mathematics 70, 23–36 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  24. Hell, P., Nešetřil, J., Zhu, X.: Duality and polynomial testing of tree homomorphisms. Transactions of the American Mathematical Society 348(4), 1281–1297 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  25. Jeavons, P.: On the algebraic structure of combinatorial problems. Theoretical Computer Science 200, 185–204 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  26. Jeavons, P., Cohen, D.A., Gyssens, M.: Closure properties of constraints. Journal of the ACM 44(4), 527–548 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. In: Proceedings of the 17th ACM Symposium on Principles of Database Systems, pp. 205–213 (1998)

    Google Scholar 

  28. Ladner, R.E.: On the structure of polynomial time reducibility. Journal of the ACM 22, 155–171 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  29. Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the 10th ACM Symposium on Theory of Computing, pp. 216–226 (1978)

    Google Scholar 

  30. Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grohe, M. (2006). The Structure of Tractable Constraint Satisfaction Problems. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_5

Download citation

  • DOI: https://doi.org/10.1007/11821069_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics