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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bulatov, A.: Combinatorial problems raised from 2-semilattices. Manuscript
Bulatov, A.A.: A Dichotomy Theorem for Constraints on a Three-Element Set. In: FOCS 2002 (2002)
Bulatov, A.: Malt’sev constraints are tractable. Technical report PRG-RR-02-05, Oxford University (2002)
Bulatov, A.A.: Tractable conservative Constraint Satisfaction Problems. In: LICS 2003 (2003)
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)
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)
Bulatov, A., Jeavons, P.: Algebraic structures in combinatorial problems. Technical report MATH-AL-4-2001, Technische Universitat Dresden (2001)
Bulatov, A., Jeavons, P.: Tractable constraints closed under a binary operation. Technical report PRG-TR-12-00, Oxford University (2000)
Dalmau, V., Pearson, J.: Set Functions and Width 1. In: Constraint Programming 1999 (1999)
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)
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)
Jeavons, P.: On the Algebraic Structure of Combinatorial Problems. Theor. Comput. Sci. 200(1-2), 185–204 (1998)
Jeavons, P.G., Cohen, D.A., Cooper, M.: Constraints, Consistency and Closure. Artificial Intelligence 101(1-2), 251–265 (1998)
Jeavons, P., Cohen, D.A., Gyssens, M.: Closure properties of constraints. J. ACM 44(4), 527–548 (1997)
Kolaitis, P.G., Vardi, M.Y.: Conjunctive-Query Containment and Constraint Satisfaction. J. Comput. Syst. Sci. 61(2), 302–332 (2000)
Kolaitis, P.G., Vardi, M.Y.: A Game-Theoretic Approach to Constraint Satisfaction. In: AAAI 2000 (2000)
Schaefer, T.: The complexity of satisfiability problems. In: Proceedings of the 10th Annual Symposium on Theory of Computing, ACM (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, H., Dalmau, V. (2004). (Smart) Look-Ahead Arc Consistency and the Pursuit of CSP Tractability. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-30201-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
Online ISBN: 978-3-540-30201-8
eBook Packages: Springer Book Archive