Skip to main content
Log in

Periodic Constraint Satisfaction Problems: Tractable Subclasses

  • Original Article
  • Published:
Constraints Aims and scope Submit manuscript

Abstract

We study a generalization of the constraint satisfaction problem (CSP), the periodic constraint satisfaction problem. An input instance of the periodic CSP is a finite set of “generating” constraints over a structured variable set that implicitly specifies a larger, possibly infinite set of constraints; the problem is to decide whether or not the larger set of constraints has a satisfying assignment. This model is natural for studying constraint networks consisting of constraints obeying a high degree of regularity or symmetry. Our main contribution is the identification of two broad polynomial-time tractable subclasses of the periodic CSP.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bulatov, A., & Jeavons, P. (2000). Tractable Constraints Closed Under a Binary Operation. Technical Report PRG-TR-12-00, Oxford University.

  2. Bulatov, A. A. (2002). A dichotomy theorem for constraints on a three-element set. In Proceedings of 43rd IEEE Symposium on Foundations of Computer Science, pages 649–658.

  3. Bulatov, A. A. (2002). Malt’sev Constraints are Tractable. Technical Report PRG-RR-02-05, Oxford University.

  4. Bulatov, A. A., Krokhin, A. A., & Jeavons, P. (2000). Constraint satisfaction problems and finite algebras. In Proceedings 27th International Colloquium on Automata, Languages, and Programming-ICALP00, volume 1853 of Lecture Notes In Computer Science, pages 272–282.

  5. Bulatov, A. A., Krokhin, A. A., & Jeavons, P. (2000). The complexity of maximal constraint languages. In ACM Symposium on Theory of Computing, pages 667–674.

  6. Cooper, M. C., Cohen, D. A., & Jeavons, P. G. (1994). Characterising tractable constraints. Artif. Intell., 65(2): 347–361.

    Google Scholar 

  7. Creignou, N., Khanna, S., & Sudan, M. (2001). Complexity Classification of Boolean Constraint Satisfaction Problems. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics.

  8. Dalmau, V., & Pearson, J. (1999). Closure functions and width 1 problems. In Principles and Practice of Constraint ProgrammingCP99, volume 1713 of Lecture Notes in Computer Science, pages 159–173. Springer-Verlag.

  9. Dalmau, V. (2000). A new tractable class of constraint satisfaction problems. In 6th International Symposium on Artificial Intelligence and Mathematics.

  10. Dalmau, V., Kolaitis, P. G., & Vardi, M. Y. (2002). Constraint satisfaction, bounded treewidth, and finite-variable logics. In Principles and Practice of Constraint Programming ‘02, Lecture Notes In Computer Science.

  11. Feder, T., & Vardi, M. Y. (1998). The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM J. Comput. 28(1): 57–104.

    Google Scholar 

  12. Freedman, M. (1998). K-sat on groups and undecidability. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 572–576.

  13. Höfting, F., & Wanke, E. (1993). Polynomial algorithms for minimum cost paths in periodic graphs. In Symposium on Discrete Algorithms, pages 493–499.

  14. Jeavons, P. (1998). On the algebraic structure of combinatorial problems. Theor. Comput. Sci. 200: 185–204.

    Google Scholar 

  15. Jeavons, P., Cohen, D., & Cooper, M. (1998). Constraints, consistency, and closure. Artif. Intell., 101(1–2): 251–265.

    Google Scholar 

  16. Jeavons, P., Cohen, D., & Pearson, J. (1998). Constraints and universal algebra. Ann. Math. Artif. Intell., 24(1–4): 51–67.

    Google Scholar 

  17. Jeavons, P. G., Cohen, D. A., & Gyssens, M. (1995). A unifying framework for tractable constraints. In Proceedings of 1st International Conference on Principles and Practice of Constraint Programming, pages 276–291. Springer-Verlag

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

    Google Scholar 

  19. Marathe, M. V., Hunt, H. B. III, Rosenkrantz, D. J., Stearns, R. E. (1998). Theory of periodically specified problems: Complexity and approximability. In Proc. 13th IEEE Conference on Computational Complexity.

  20. Marathe, M. V., Hunt, H. B. III, Stearns, R. E., & Radhakrishnan, V. (1998). Approximation algorithms for PSPACE–hard hierarchically and periodically specified problems. SIAM J. Comput., 27(5): 1237–1261.

    Google Scholar 

  21. Orlin, J. (1981). The complexity of dynamic languages and dynamic optimization problems. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 218–227.

  22. Pearson, J. K., Jeavons, P. G. (1997). A survey of tractable constraint satisfaction problems. Technical report, Royal Holloway, University of London

  23. Schaefer, T. J. (1978). The complexity of satisfiability problems. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 216–226.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hubie Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, H. Periodic Constraint Satisfaction Problems: Tractable Subclasses. Constraints 10, 97–113 (2005). https://doi.org/10.1007/s10601-005-0551-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-005-0551-z

Keywords

Navigation