Maintaining Arc-Consistency within Dynamic Backtracking

  • Narendra Jussien
  • Romuald Debruyne
  • Patrice Boizumault
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1894)


Most of complete search algorithms over Constraint Satisfaction Problems (csp) are based on Standard Backtracking. Two main enhancements of this basic scheme have been studied: first, to integrate constraint propagation as mac which maintains arc consistency during search; second, intelligent backtrackers which avoid repeatedly falling in the same dead-ends by recording nogoods as Conflict-directed Back Jumping (cbj) or Dynamic Backtracking (dbt). Integrations of constraint propagation within intelligent backtrackers have been done as mac-cbj which maintains arc consistency in cbj. However, Bessière and Régin have shown that mac-cbj was very rarely better than mac. However, the inadequacy of mac-cbj is more related to the fact that cbj does not avoid thrashing than to the cost of the management of nogoods.

This paper describes and evaluates mac-dbt which maintains arc-consistency in dbt. Experiments show that mac-dbt is able to solve very large problems and that it remains very stable as the size of the problems increases. Moreover, mac-dbt outperforms mac on the structured problems we have randomly generated.


Constraint Satisfaction Problem Constraint Propagation Partial Assignment Current Partial Assignment Open Shop Problem 
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  1. 1.
    Andrew B. Baker. The hazards of fancy backtracking. In 12th National Conf. on Artificial Intelligence, AAAI94, pages 288–293, Seattle, WA, USA, 1994.Google Scholar
  2. 2.
    Roberto Bayardo Jr. and Robert Schrag. Using CSP look-back techniques to solve exceptionnaly hard SAT instances. In CP’96, 1996.Google Scholar
  3. 3.
    Roberto J. Bayardo Jr. and Daniel P. Miranker. A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem. In AAAI’96, 1996.Google Scholar
  4. 4.
    Christian Bessière. Arc consistency in dynamic constraint satisfaction problems. In Proceedings AAAI’91, 1991.Google Scholar
  5. 5.
    Christian Bessière and Jean-Charles Régin. MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problem. In CP’96, Cambridge, MA, 1996.Google Scholar
  6. 6.
    C. Bliek. Generalizing partial order and dynamic backtracking. In Proceedings of AAAI, 1998.Google Scholar
  7. 7.
    Romuald Debruyne. Arc-consistency in dynamic CSPs is no more prohibitive. In 8th Conference on Tools with Artificial Intelligence (TAI’96), pages 299–306, Toulouse, France, 1996.Google Scholar
  8. 8.
    Romuald Debruyne. Local consistencies for large CSPs. PhD thesis, Université de Montpellier II, December18 1998. In French.Google Scholar
  9. 9.
    Romuald Debruyne and Christian Bessière. From restricted path consistency to max-restricted path consistency. In CP’97, pages 312–326, Linz, Austria, October 1997.Google Scholar
  10. 10.
    Matthew L. Ginsberg. Dynamic backtracking. Journal of Artificial Intelligence Research, 1:25–46, 1993.zbMATHGoogle Scholar
  11. 11.
    Matthew L. Ginsberg and David A McAllester. Gsat and dynamic backtracking. In International Conference on the Principles of Knowledge Representation (KR94), pages 226–237, 1994.Google Scholar
  12. 12.
    Narendra Jussien. Relaxation de contraintes pour les CSP dynamiques. PhD thesis, Université de Rennes I, October24 1997. In French.Google Scholar
  13. 13.
    Narendra Jussien and Christelle Guéret. Improving branch and bound algorithms for open shop problems. In Conference of the International Federation of Operational Research Societies (IFORS’99), Beijing, China, August 1999.Google Scholar
  14. 14.
    Narendra Jussien and Olivier Lhomme. Dynamic domain splitting for numeric csp. In European Conference on Artificial Intelligence, pages 224–228, Brighton, United Kingdom, August 1998.Google Scholar
  15. 15.
    Narendra Jussien and Olivier Lhomme. The path-repair algorithm. In CP99 Post-conference workshop on Large scale combinatorial optimisation and constraints, Alexandria, VA, USA, October 1999.Google Scholar
  16. 16.
    Patrick Prosser. MAC-CBJ: maintaining arc-consistency with conflict-directed backjumping. Research Report 95/177, Department of Computer Science-University of Strathclyde, 1995.Google Scholar
  17. 17.
    Jean-Charles Régin. Développement d’outils algorithmiques pour l’Intelligence Artificielle. Application à la chimie organique. Thèse de doctorat, Université de Montpellier II, 21 December 1995. In French.Google Scholar
  18. 18.
    Daniel Sabin and Eugene Freuder. Contradicting conventional wisdom in constraint satisfaction. In Alan Borning, editor, Principles and Practice of Constraint Programming, volume 874 of Lecture Notes in Computer Science. Springer, May 1994. (PPCP’94: Second International Workshop, Orcas Island, Seattle, USA).Google Scholar
  19. 19.
    Thomas Schiex and Gérard Verfaillie. Nogood Recording fot Static and Dynamic Constraint Satisfaction Problems. International Journal of Artificial Intelligence Tools, 3(2):187–207, 1994.CrossRefGoogle Scholar
  20. 20.
    R. M. Stallman and G. J. Sussman. Forward reasoning and dependency directed backtracking in a system for computer-aided circuit analysis. Artificial Intelligence, 9:135–196, 1977.zbMATHCrossRefGoogle Scholar
  21. 21.
    Gérard Verfaillie and Thomas Schiex. Dynamic backtracking for dynamic csps. In Thomas Schiex and Christian Bessière, editors, Proceedings ECAI’94 Workshop on Constraint Satisfaction Issues raised by Practical Applications, Amsterdam, August 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Narendra Jussien
    • 1
  • Romuald Debruyne
    • 1
  • Patrice Boizumault
    • 1
  1. 1.École des Mines de NantesNantes Cedex 3

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