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International Conference on Principles and Practice of Constraint Programming

CP 2016: Principles and Practice of Constraint Programming pp 130–146Cite as

The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9892))

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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Author information

Authors and Affiliations

  1. CNRS, LAAS, 7 avenue du colonel Roche, 31400, Toulouse, France

    Clément Carbonnel

  2. University of Toulouse, INP Toulouse, LAAS, 31400, Toulouse, France

    Clément Carbonnel

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  1. Clément Carbonnel
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Correspondence to Clément Carbonnel .

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Editors and Affiliations

  1. University of Nice Sophia Antipolis , Sophia Antipolis, France

    Michel Rueher

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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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  • DOI: https://doi.org/10.1007/978-3-319-44953-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44952-4

  • Online ISBN: 978-3-319-44953-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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