The Order Encoding: From Tractable CSP to Tractable SAT

  • Justyna Petke
  • Peter Jeavons
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6695)


Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). The general CSP is known to be NP-complete, but many different conditions have been identified which are sufficient to ensure that classes of instances satisfying those conditions are tractable, that is, solvable in polynomial time [1,2,3,4,7].


Constraint Satisfaction Problem Boolean Variable Constraint Language Lower Domain Order Encode 
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.


  1. 1.
    Cohen, D., Jeavons, P.: The complexity of constraint languages. In: Handbook of Constraint Programming, ch. 8, pp. 245–280. Elsevier, Amsterdam (2006)CrossRefGoogle Scholar
  2. 2.
    Cohen, D., et al.: Building tractable disjunctive constraints. Journal of the ACM 47, 826–853 (2000)CrossRefzbMATHGoogle Scholar
  3. 3.
    Deville, Y., et al.: Constraint satisfaction over connected row convex constraints. In: Proceedings of IJCAI 1997, pp. 405–411 (1997)Google Scholar
  4. 4.
    Jeavons, P., Cooper, M.C.: Tractable constraints on ordered domains. Artificial Intelligence Journal, 327–339 (1995)Google Scholar
  5. 5.
    Petke, J., Jeavons, P.: Local consistency and SAT-solvers. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 398–413. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Prestwich, S.D.: CNF encodings. In: Handbook of Satisfiability, ch. 2, pp. 75–97. IOS Press, Amsterdam (2009)Google Scholar
  7. 7.
    Schaefer, T.J.: The Complexity of Satisfiability Problems. In: Proceedings of the 10th ACM Symposium on Theory of Computing - STOC 1978, pp. 216–226. ACM, New York (1978)Google Scholar
  8. 8.
    Tamura, N., et al.: Compiling finite linear CSP into SAT. Constraints Journal 14, 254–272 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Justyna Petke
    • 1
  • Peter Jeavons
    • 1
  1. 1.Computing LaboratoryOxford UniversityOxfordUK

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