Abstract
The class of constraint satisfaction problems (CSPs) over finite domains has been shown to be NP-complete, but many tractable subclasses have been identified in the literature. In this paper we are interested in restrictions on the types of constraint relations in CSP instances. By a result of Jeavons et al. we know that a key to the complexity of classes arising from such restrictions is the closure properties of the sets of relations. It has been shown that sets of relations that are closed under constant, majority, affine, or associative, commutative, and idempotent (ACI) functions yield tractable subclasses of CSP. However, it has been unknown whether other closure properties may generate tractable subclasses.
In this paper we introduce a class of tractable (in fact, SL-complete) CSPs based on bipartite graphs. We show that there are members of this class that are not closed under constant, majority, affine, or ACI functions, and that it, therefore, is incomparable with previously identified classes.
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References
Cooper, M., Cohen, D., Jeavons, P.: Characterizing tractable constraints. Artificial Intelligence 65, 347–361 (1994)
Deville, Y., Barette, O., Van Hentenryck, P.: Constraint satisfaction over connected row convex constraints. In: Pollack, M.E. (ed.) Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, Nagoya, Japan. Morgan Kaufmann, San Francisco (1997)
Feder, T., Vardi, M.Y.: The computational structure of monotone monadic snp and constraint satisfaction: a study through Datalog and group theory. SIAM Journal of Computing 28(1), 57–104 (1998)
Freuder, E.C.: Synthesizing constraint expressions. Communications of the ACM 21, 958–966 (1978)
Freuder, E.C.: A sufficient condition for backtrack-free search. Journal of the ACM 29(1), 24–32 (1982)
Hell, P., Nešetřil, J.: On the complexity of H-coloring. Journal of Combinatorial Theory, ser. B 48, 92–110 (1990)
Jeavons, P., Cohen, D., Cooper, M.: Constraints, consistency, and closure. Artificial Intelligence 101(1-2), 251–265 (1998)
Jeavons, P., Cohen, D., Gyssens, M.: Closure properties of constraints. Journal of the ACM 44, 527–548 (1997)
Jeavons, P., Cohen, D., Pearson, J.: Constraints and universal algebra. Annals of Mathematics and Artificial Intelligence (1999) (to appear)
Jeavons, P., Cooper, M.: Tractable constraints in ordered domains. Artificial Intelligence 79, 327–339 (1996)
Reif, J.H.: Symmetric complementation. In: Proceedings of the 14th ACM Symposium on Theory of Computing, pp. 210–214 (1982)
Montanari, U.: Networks of constraints: fundamental properties and applications to picture processing. Information Sciences 7, 95–132 (1974)
Nisan, N., Ta-Schma, A.: Symmetric logspace is closed under complement. In: Proceedings of the 27th ACM Symposium on Theory of Computing, STOC 1995 (1995)
Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the Tenth ACM Symposium on Theory of Computing, pp. 216–226 (1978)
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Bjäreland, M., Jonsson, P. (1999). Exploiting Bipartiteness to Identify Yet Another Tractable Subclass of CSP. In: Jaffar, J. (eds) Principles and Practice of Constraint Programming – CP’99. CP 1999. Lecture Notes in Computer Science, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48085-3_9
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DOI: https://doi.org/10.1007/978-3-540-48085-3_9
Publisher Name: Springer, Berlin, Heidelberg
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