Skip to main content
SpringerLink
Log in

High-Order Consistency in Valued Constraint Satisfaction

  • Published:
Constraints Aims and scope Submit manuscript

Abstract

k-consistency operations in constraint satisfaction problems (CSPs) render constraints more explicit by solving size-k subproblems and projecting the information thus obtained down to low-order constraints. We generalise this notion of k-consistency to valued constraint satisfaction problems (VCSPs) and show that it can be established in polynomial time when penalties lie in a discrete valuation structure.

A generic definition of consistency is given which can be tailored to particular applications. As an example, a version of high-order consistency (face consistency) is presented which can be established in low-order polynomial time given certain restrictions on the valuation structure and the form of the constraint graph.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bertele, U., & Brioschi, F. (1972). Nonserial Dynamic Programming. Academic Press, New York, NY, USA.

    Google Scholar 

  2. Bistarelli, S., Fargier, H., Montanari, U., Rossi, F., Schiex, T., & Verfaillie, G. (1999). Semiring-based CSPs and valued CSPs: Frameworks, properties and comparison. Constraints 4: 199–240.

    Article  Google Scholar 

  3. Cooper, M. C. (1990). An optimal k-consistency algorithm. Artif. Intell. 41: 89–95.

    Article  Google Scholar 

  4. Cooper, M. C. (1993). Interpretation of line drawings of complex objects. Image Vis. Comput. 11(2): 82–90.

    Article  Google Scholar 

  5. Cooper, M. C. (1999). Linear-time algorithms for testing the realisability of line drawings of curved objects. Artif. Intell. 108: 31–67.

    Article  Google Scholar 

  6. Cooper, M. C. (2003). Reduction operations in fuzzy and valued constraint satisfaction. Fuzzy Sets Syst. 134: 311–342.

    Article  Google Scholar 

  7. Cooper, M. C. (2004). Cyclic consistency: A local reduction operation for binary valued constraints. Artif. Intell. 155(1–2): 69–92.

    Article  Google Scholar 

  8. Cooper M. C. (2005). High-Order Consistency in Valued Constraint Satisfaction. Internal Report, IRIT, Université Toulouse III.

  9. Cooper, M. C., & Schiex, T. (2004). Arc consistency for soft constraints. Artif. Intell. 154(1–2): 199–227.

    Article  Google Scholar 

  10. Dechter, R. (1997). Mini-buckets: A general scheme for generating approxiamtions in automated reasoning. In Proc. IJCAI-97, Nagoya, Japan, pages 1297–1303.

  11. Dechter, R. (2003). Constraint Processing. San Mateo, CA: Morgan Kaukmann.

    Google Scholar 

  12. Dechter, R., & Pearl, J. (1988). Network-based heuristics for constraint satisfaction problems. Artif. Intell. 34: 1–38.

    Article  Google Scholar 

  13. Fargier, H., & Lang, J. (1993). Uncertainty in constraint satisfaction problems: A probabilistic approach. In Proc. ECSQARU, Springer-Verlag, LNCS 747, pages 97–104.

  14. Fargier, H., Lang, J., & Schiex, T. (1993). Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems. In Proc. of the 1st European Congress on Fuzzy and Intelligent Technologies.

  15. Larkin, D. (2003). Semi-Independent Partitioning: A method for bounding the solution to COP’s. In Proc. Principles and Practice of Constraint Propgramming—CP 2003, Springer-Verlag, LNCS 2833, pages 894–898.

  16. Larrosa, J. (2002). On arc and node consistency in weighted CSP. In Proc. AAAI‘02.

  17. Larrosa, J., & Schiex, T. (2003). In the Quest of the Best Form of Local Consistency for Weighted CSP. IJCAI.

  18. Rosenfeld, A., Hummel, R., & Zucker, S. (1976). Scene labelling by relaxation operations. IEEE Trans. Syst. Man Cybern. 6(6): 173–184.

    Google Scholar 

  19. Schiex, T. (2000). Arc consistency for soft constraints. In Proc. CP’2000, LNCS 1894, pages 411–424.

  20. Schiex, T., Fargier, H., & Verfaillie, G. (1995). Valued constraint satisfaction problems: hard and easy problems. In Proc. of the 14th IJCAI, Montreal, Canada, pages 631–637.

Download references

Author information

Authors and Affiliations

  1. IRIT, University of Toulouse III, 118 route de Narbonne, 31062, Toulouse, France

    Martin C. Cooper

Authors
  1. Martin C. Cooper
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin C. Cooper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cooper, M.C. High-Order Consistency in Valued Constraint Satisfaction. Constraints 10, 283–305 (2005). https://doi.org/10.1007/s10601-005-2240-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-005-2240-3

Keywords

Search

Navigation