Adaptive Parameterized Consistency for Non-binary CSPs by Counting Supports

  • Robert J. Woodward
  • Anthony Schneider
  • Berthe Y. Choueiry
  • Christian Bessiere
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8656)


Determining the appropriate level of local consistency to enforce on a given instance of a Constraint Satisfaction Problem (CSP) is not an easy task. However, selecting the right level may determine our ability to solve the problem. Adaptive parameterized consistency was recently proposed for binary CSPs as a strategy to dynamically select one of two local consistencies (i.e., AC and maxRPC). In this paper, we propose a similar strategy for non-binary table constraints to select between enforcing GAC and pairwise consistency. While the former strategy approximates the supports by their rank and requires that the variables domains be ordered, our technique removes those limitations. We empirically evaluate our approach on benchmark problems to establish its advantages.


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  1. 1.
    Balafrej, A., Bessiere, C., Coletta, R., Bouyakhf, E.H.: Adaptive Parameterized Consistency. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 143–158. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Bessiere, C.: Constraint Propagation. In: Handbook of Constraint Programming, pp. 29–83. Elsevier (2006)Google Scholar
  3. 3.
    Bessière, C., Régin, J.C., Yap, R.H., Zhang, Y.: An Optimal Coarse-Grained Arc Consistency Algorithm. Artificial Intelligence 165(2), 165–185 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bessière, C., Stergiou, K., Walsh, T.: Domain Filtering Consistencies for Non-Binary Constraints. Artificial Intelligence 172, 800–822 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting Systematic Search by Weighting Constraints. In: Proc. ECAI 2004, pp. 146–150 (2004)Google Scholar
  6. 6.
    Debruyne, R., Bessière, C.: From Restricted Path Consistency to Max-Restricted Path Consistency. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 312–326. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Geschwender, D., Karakashian, S., Woodward, R., Choueiry, B.Y., Scott, S.D.: Selecting the Appropriate Consistency Algorithm for CSPs Using Machine Learning Techniques. In: Proc. of AAAI 2013, pp. 1611–1612 (2013)Google Scholar
  8. 8.
    Gyssens, M.: On the Complexity of Join Dependencies. ACM Trans. Database Systems 11(1), 81–108 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Haralick, R.M., Elliott, G.L.: Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Artificial Intelligence 14, 263–313 (1980)CrossRefGoogle Scholar
  10. 10.
    Janssen, P., Jégou, P., Nougier, B., Vilarem, M.C.: A Filtering Process for General Constraint-Satisfaction Problems: Achieving Pairwise-Consistency Using an Associated Binary Representation. In: IEEE Workshop on Tools for AI, pp. 420–427 (1989)Google Scholar
  11. 11.
    Kadioglu, S., Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm Selection and Scheduling. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 454–469. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Karakashian, S., Woodward, R., Reeson, C., Choueiry, B.Y., Bessiere, C.: A First Practical Algorithm for High Levels of Relational Consistency. In: Proc. AAAI 2010, pp. 101–107 (2010)Google Scholar
  13. 13.
    Lecoutre, C.: STR2: Optimized Simple Tabular Reduction for Table Constraints. Constraints 16(4), 341–371 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Lecoutre, C., Likitvivatanavong, C., Yap, R.H.C.: A Path-Optimal GAC Algorithm for Table Constraints. In: Proc. of ECAI 2012, pp. 510–515 (2012)Google Scholar
  15. 15.
    Lecoutre, C., Paparrizou, A., Stergiou, K.: Extending STR to a Higher-Order Consistency. In: Proc. AAAI 2013, Bellevue, WA, pp. 576–582 (2013)Google Scholar
  16. 16.
    Mackworth, A.K.: Consistency in Networks of Relations. AI 8, 99–118 (1977)zbMATHGoogle Scholar
  17. 17.
    Mohr, R., Masini, G.: Good Old Discrete Relaxation. In: European Conference on Artificial Intelligence (ECAI 1988), pp. 651–656. W. Germany, Munich (1988)Google Scholar
  18. 18.
    Paparrizou, A., Stergiou, K.: Evaluating Simple Fully Automated Heuristics for Adaptive Constraint Propagation. In: Proc. of ICTAI 2012, pp. 880–885 (2012)Google Scholar
  19. 19.
    Pesant, G., Quimper, C.G., Zanarini, A.: Counting-Based Search: Branching Heuristics for Constraint Satisfaction Problems. JAIR 43, 173–210 (2012)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Stergiou, K.: Heuristics for Dynamically Adapting Propagation. In: Proc. of ECAI 2008, pp. 485–489 (2008)Google Scholar
  21. 21.
    Ullmann, J.R.: Partition Search for Non-binary Constraint Satisfaction. Information Sciences 177(18), 3639–3678 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: Portfolio-Based Algorithm Selection for SAT. JAIR 32, 565–606 (2008)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Robert J. Woodward
    • 1
    • 2
  • Anthony Schneider
    • 1
  • Berthe Y. Choueiry
    • 1
  • Christian Bessiere
    • 2
  1. 1.Constraint Systems LaboratoryUniversity of Nebraska-LincolnUSA
  2. 2.CNRSUniversity of MontpellierFrance

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