Abstract
Given a fixed constraint language \(\varGamma \), the conservative CSP over \(\varGamma \) (denoted by c-CSP(\(\varGamma \))) is a variant of CSP(\(\varGamma \)) where the domain of each variable can be restricted arbitrarily. In [5] a dichotomy has been proven for conservative CSP: for every fixed language \(\varGamma \), c-CSP(\(\varGamma \)) is either in P or NP-complete. However, the characterization of conservatively tractable languages is of algebraic nature and the recognition algorithm provided in [5] is super-exponential in the domain size. The main contribution of this paper is a polynomial-time algorithm that, given a constraint language \(\varGamma \) as input, decides if c-CSP(\(\varGamma \)) is tractable. In addition, if \(\varGamma \) is proven tractable the algorithm also outputs its coloured graph, which contains valuable information on the structure of \(\varGamma \).
Supported by ANR Project ANR-10-BLAN-0210.
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Carbonnel, C. (2016). The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_9
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