On the Computational Complexity of Monotone Constraint Satisfaction Problems

  • Miki Hermann
  • Florian Richoux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5431)


Constraint Satisfaction Problems (csp) constitute a convenient way to capture many combinatorial problems. The general csp is known to be NP-complete, but its complexity depends on a parameter, usually a set of relations, upon which they are constructed. Following the parameter, there exist tractable and intractable instances of csps. In this paper we show a dichotomy theorem for every finite domain of csp including also disjunctions. This dichotomy condition is based on a simple condition, allowing us to classify monotone csps as tractable or NP-complete. We also prove that the meta-problem, verifying the tractability condition for monotone constraint satisfaction problems, is fixed-parameter tractable. Moreover, we present a polynomial-time algorithm to answer this question for monotone csps over ternary domains.


Computational Complexity Constant Function Unary Function Domain Size Constraint Satisfaction Problem 


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  1. 1.
    Bulatov, A.A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. Journal of the Association for Computing Machinery 53(1), 66–120 (2006)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Cohen, D., Jeavons, P., Jonsson, P., Koubarakis, M.: Building tractable disjunctive constraints. Journal of the Association for Computing Machinery 47(5), 826–853 (2000)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Downey, R.G., Fellows, M.R.: Parametrized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  4. 4.
    Feder, T., Vardi, M.Y.: The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM Journal on Computing 28(1), 57–104 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Jeavons, P.: On the algebraic structure of combinatorial problems. Theoretical Computer Science 200(1-2), 185–204 (1998)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Krasner, M.: Une généralisation de la notion de corps. Journal de Mathématiques pures et appliquées 17, 367–385 (1938)MATHGoogle Scholar
  7. 7.
    Pöschel, R.: Galois connections for operations and relations. In: Denecke, K., et al. (eds.) Galois Connections and Applications, pp. 231–258. Kluwer, Dordrecht (2004)CrossRefGoogle Scholar
  8. 8.
    Salomaa, A.: Composition sequences for functions over a finite domain. Theoretical Computer Science 292(1), 263–281 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings 10th Symposium on Theory of Computing (STOC 1978), San Diego, California, USA, pp. 216–226 (1978)Google Scholar
  10. 10.
    Yanov, Y.I., Muchnik, A.A.: On the existence of k-valued closed classes that have no bases. Doklady Akademii Nauk SSSR 127, 44–46 (1959) (in Russian)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Miki Hermann
    • 1
  • Florian Richoux
    • 1
  1. 1.LIX (CNRS, UMR 7161), École PolytechniquePalaiseauFrance

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