Skip to main content
Log in

Three generalizations of the FOCUS constraint

  • Published:
Constraints Aims and scope Submit manuscript

Abstract

The FOCUS constraint expresses the notion that solutions are concentrated. In practice, this constraint suffers from the rigidity of its semantics. To tackle this issue, we propose three generalizations of the FOCUS constraint. We provide for each one a complete filtering algorithm. Moreover, we propose ILP and CSP decompositions.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. Recall that the average CPU includes only the runtime of the successful runs.

References

  1. Ahuja, R.K., Magnanti, T.L., & Orlin, J.B. (1993). Network flows: Theory, algorithms, and applications.

  2. Boussemart, F., Hemery, F., Lecoutre, C., & Sais, L. (2004). Boosting systematic search by weighting constraints. In Proceedings of the 16th European Conference on Artificial Intelligence (ECAI’04) (pp. 482–486).

  3. Dasgupta, S., Papadimitriou, C.H., & Vazirani, U.V. (2006). Algorithms. McGraw-Hill.

  4. De Clercq, A., Petit, T., Beldiceanu, N., & Jussien, N. (2011). Filtering algorithms for discrete cumulative problems with overloads of resource. In Proceedings of the 17th International Conference on Principles and Practice of Constraint Programming (CP’11) (pp. 240–255).

  5. Demassey, S., Pesant, G., & Rousseau, L-M. (2006). A cost-regular based hybrid column generation approach. Constraints, 11(4), 315–333.

    Article  MathSciNet  MATH  Google Scholar 

  6. Maher, M., Narodytska, N., Quimper, C-G., & Walsh, T. (2008). Flow-based propagators for the sequence and related global constraints. In Proceedings of the 14th International Conference on Principles and Practice of Constraint Programming (CP’08) (pp. 159–174).

  7. Pesant, G. (2004). A regular language membership constraint for finite sequences of variables. In Proceedings of the 10th International Conference on Principles and Practice of Constraint Programming (CP’04) (pp. 482–495).

  8. Pesant, G. (2001). A filtering algorithm for the stretch constraint. In Proceedings of the 10th International Conference on Principles and Practice of Constraint Programming (CP’01) (pp. 183–195).

  9. Pesant, G., & Spread, J.-C. Régin. (2005). A balancing constraint based on statistics. In Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming (CP’05) (pp. 460–474).

  10. Petit, T., & Poder, E. (2008). Global propagation of practicability constraints. In Proc. CPAIOR, volume 5015 (pp. 361–366).

  11. Petit, T., & Régin, J.-C. (2011). The ordered distribute constraint. International Journal on Artificial Intelligence Tools, 20(4), 617–637.

    Article  Google Scholar 

  12. Petit, T. (2012). Focus: A constraint for concentrating high costs. In Proceedings of the 18th International Conference on Principles and Practice of Constraint Programming (CP’12).

  13. Régin, J.-C. (1994). A filtering algorithm for constraints of difference in CSPs. In Proceedings of the 12th National Conference on Artificial intelligence (AAAI’94) (Vol. 1, pp. 362–367). American Association for Artificial Intelligence.

  14. Régin, J.-C. (1996). Generalized arc consistency for global cardinality constraint. In Proceedings of the 14th National Conference on Artificial intelligence (AAAI’98) (pp. 209–215).

  15. Régin, J.-C. (2001). Minimization of the number of breaks in sports scheduling problems using constraint programming. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 57, 115–130.

    MathSciNet  MATH  Google Scholar 

  16. Rossi, F., van Beek, P., & Walsh, T. (2006). Handbook of constraint programming (Foundations of Artificial Intelligence). New York: Elsevier Science Inc.

    MATH  Google Scholar 

  17. Schaus, P., Deville, Y., Dupont, P., & Régin, J-C. (2007). The deviation constraint. In Proc. CPAIOR (Vol. 4510, pp. 260–274).

  18. Schaus, P., Van Hentenryck, P., & Régin, J.-C. (2009). Scalable load balancing in nurse to patient assignment problems. In Proc. CPAIOR, volume 5547 of Lecture Notes in Computer Science (pp. 248–262). Springer.

  19. Wagner, A., & Harvey, M. (1962). Optimal capacity scheduling I. Operations Research, 10(4), 518–532.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohamed Siala.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narodytska, N., Petit, T., Siala, M. et al. Three generalizations of the FOCUS constraint. Constraints 21, 495–532 (2016). https://doi.org/10.1007/s10601-015-9233-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-015-9233-7

Keywords

Navigation