(Smart) Look-Ahead Arc Consistency and the Pursuit of CSP Tractability

  • Hubie Chen
  • Víctor Dalmau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3258)

Abstract

The constraint satisfaction problem (CSP) can be formulated as the problem of deciding, given a pair (A,B) of relational structures, whether or not there is a homomorphism from A to B. Although the CSP is in general intractable, it may be restricted by requiring the “target structure” B to be fixed; denote this restriction by CSP(B). In recent years, much effort has been directed towards classifying the complexity of all problems CSP(B). The acquisition of CSP(B) tractability results has generally proceeded by isolating a class of relational structures B believed to be tractable, and then demonstrating a polynomial-time algorithm for the class. In this paper, we introduce a new approach to obtaining CSP(B) tractability results: instead of starting with a class of structures, we start with an algorithm called look-ahead arc consistency, and give an algebraic characterization of the structures solvable by our algorithm. This characterization is used both to identify new tractable structures and to give new proofs of known tractable structures.

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References

  1. 1.
    Bulatov, A.: Combinatorial problems raised from 2-semilattices. ManuscriptGoogle Scholar
  2. 2.
    Bulatov, A.A.: A Dichotomy Theorem for Constraints on a Three-Element Set. In: FOCS 2002 (2002)Google Scholar
  3. 3.
    Bulatov, A.: Malt’sev constraints are tractable. Technical report PRG-RR-02-05, Oxford University (2002)Google Scholar
  4. 4.
    Bulatov, A.A.: Tractable conservative Constraint Satisfaction Problems. In: LICS 2003 (2003)Google Scholar
  5. 5.
    Bulatov, A.A., Krokhin, A.A., Jeavons, P.: Constraint Satisfaction Problems and Finite Algebras. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, p. 272. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Bulatov, A., Jeavons, P.: An Algebraic Approach to Multi-sorted Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 183–198. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Bulatov, A., Jeavons, P.: Algebraic structures in combinatorial problems. Technical report MATH-AL-4-2001, Technische Universitat Dresden (2001)Google Scholar
  8. 8.
    Bulatov, A., Jeavons, P.: Tractable constraints closed under a binary operation. Technical report PRG-TR-12-00, Oxford University (2000)Google Scholar
  9. 9.
    Dalmau, V., Pearson, J.: Set Functions and Width 1. In: Constraint Programming 1999 (1999)Google Scholar
  10. 10.
    del Val, A.: On 2SAT and Renamable Horn. In: AAAI 2000, Proceedings of the Seventeenth (U.S.) National Conference on Artificial Intelligence, Austin, Texas, pp. 279–284 (2000)Google Scholar
  11. 11.
    Feder, T., Vardi, M.Y.: The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory. SIAM J. Comput. 28(1), 57–104 (1998)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Jeavons, P.: On the Algebraic Structure of Combinatorial Problems. Theor. Comput. Sci. 200(1-2), 185–204 (1998)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jeavons, P.G., Cohen, D.A., Cooper, M.: Constraints, Consistency and Closure. Artificial Intelligence 101(1-2), 251–265 (1998)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Jeavons, P., Cohen, D.A., Gyssens, M.: Closure properties of constraints. J. ACM 44(4), 527–548 (1997)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kolaitis, P.G., Vardi, M.Y.: Conjunctive-Query Containment and Constraint Satisfaction. J. Comput. Syst. Sci. 61(2), 302–332 (2000)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kolaitis, P.G., Vardi, M.Y.: A Game-Theoretic Approach to Constraint Satisfaction. In: AAAI 2000 (2000)Google Scholar
  17. 17.
    Schaefer, T.: The complexity of satisfiability problems. In: Proceedings of the 10th Annual Symposium on Theory of Computing, ACM (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hubie Chen
    • 1
  • Víctor Dalmau
    • 2
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.Departament de TecnologiaUniversitat Pompeu FabraBarcelonaSpain

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