Global Inverse Consistency for Interactive Constraint Satisfaction

  • Christian Bessiere
  • Hélène Fargier
  • Christophe Lecoutre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)


Some applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples.


Constraint Satisfaction Constraint Programming Interactive Resolution Constraint Network Oracle Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Amilhastre, J., Fargier, H., Marquis, P.: Consistency restoration and explanations in dynamic CSPs - application to configuration. Artificial Intelligence 135(1-2), 199–234 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Astesana, J.M., Cosserat, L., Fargier, H.: Constraint-based vehicle configuration: A case study. In: Proceedings of ICTAI 2010, pp. 68–75 (2010)Google Scholar
  3. 3.
    Bessiere, C., Meseguer, P., Freuder, E.C., Larrosa, J.: On Forward Checking for non-binary constraint satisfaction. Artificial Intelligence 141, 205–224 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: Proceedings of ECAI 2004, pp. 146–150 (2004)Google Scholar
  5. 5.
    Debruyne, R., Bessiere, C.: Domain filtering consistencies. Journal of Artificial Intelligence Research 14, 205–230 (2001)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Freuder, E.C., Elfe, C.D.: Neighborhood inverse consistency preprocessing. In: Proceedings of AAAI 1996, Portland, Oregon, pp. 202–208 (1996)Google Scholar
  7. 7.
    Gelle, E., Weigel, R.: Interactive configuration using constraint satisfaction techniques. In: Proceedings of PACT 1996, pp. 37–44 (1996)Google Scholar
  8. 8.
    Gottlob, G.: On minimal constraint networks. Artificial Intelligence 191-192, 42–60 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hadzic, T., Andersen, H.R.: Interactive reconfiguration in power supply restoration. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 767–771. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Hadzic, T., Hansen, E.R., O’Sullivan, B.: Layer compression in decision diagrams. In: Proceedings of ICTAI 2008, pp. 19–26 (2008)Google Scholar
  11. 11.
    Hebrard, E., Hnich, B., O’Sullivan, B., Walsh, T.: Finding diverse and similar solutions in constraint programming. In: Proceedings of AAAI 2005, pp. 372–377 (2005)Google Scholar
  12. 12.
    Janssen, P., Jégou, P., Nouguier, B., Vilarem, M.C., Castro, B.: SYNTHIA: Assisted design of peptide synthesis plans. New Journal of Chemistry 14(12), 969–976 (1990)Google Scholar
  13. 13.
    Lecoutre, C.: STR2: Optimized simple tabular reduction for table constraints. Constraints 16(4), 341–371 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lecoutre, C., Hemery, F.: A study of residual supports in arc consistency. In: Proceedings of IJCAI 2007, pp. 125–130 (2007)Google Scholar
  15. 15.
    Martinez, D.: Résolution interactive de problemes de satisfaction de contraintes. PhD thesis, Supaero, Toulouse, France (1998)Google Scholar
  16. 16.
    Papadimitriou, C.: Private communication (1999)Google Scholar
  17. 17.
    Sabin, D., Freuder, E.C.: Contradicting conventional wisdom in constraint satisfaction. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874, pp. 10–20. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  18. 18.
    Ullmann, J.R.: Partition search for non-binary constraint satisfaction. Information Science 177, 3639–3678 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: Random constraint satisfaction: easy generation of hard (satisfiable) instances. Artificial Intelligence 171(8-9), 514–534 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Xu, K., Li, W.: Exact phase transitions in random constraint satisfaction problems. Journal of Artificial Intelligence Research 12, 93–103 (2000)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christian Bessiere
    • 1
  • Hélène Fargier
    • 2
  • Christophe Lecoutre
    • 3
  1. 1.LIRMM-CNRSUniversity of MontpellierFrance
  2. 2.IRIT-CNRSUniversity of ToulouseFrance
  3. 3.CRIL-CNRSUniversity of ArtoisLensFrance

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