(Smart) Look-Ahead Arc Consistency and the Pursuit of CSP Tractability
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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- 1.Bulatov, A.: Combinatorial problems raised from 2-semilattices. ManuscriptGoogle Scholar
- 2.Bulatov, A.A.: A Dichotomy Theorem for Constraints on a Three-Element Set. In: FOCS 2002 (2002)Google Scholar
- 3.Bulatov, A.: Malt’sev constraints are tractable. Technical report PRG-RR-02-05, Oxford University (2002)Google Scholar
- 4.Bulatov, A.A.: Tractable conservative Constraint Satisfaction Problems. In: LICS 2003 (2003)Google Scholar
- 7.Bulatov, A., Jeavons, P.: Algebraic structures in combinatorial problems. Technical report MATH-AL-4-2001, Technische Universitat Dresden (2001)Google Scholar
- 8.Bulatov, A., Jeavons, P.: Tractable constraints closed under a binary operation. Technical report PRG-TR-12-00, Oxford University (2000)Google Scholar
- 9.Dalmau, V., Pearson, J.: Set Functions and Width 1. In: Constraint Programming 1999 (1999)Google Scholar
- 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
- 16.Kolaitis, P.G., Vardi, M.Y.: A Game-Theoretic Approach to Constraint Satisfaction. In: AAAI 2000 (2000)Google Scholar
- 17.Schaefer, T.: The complexity of satisfiability problems. In: Proceedings of the 10th Annual Symposium on Theory of Computing, ACM (1978)Google Scholar