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Backdoors to Tractable Valued CSP

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Principles and Practice of Constraint Programming (CP 2016)

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

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Abstract

We extend the notion of a strong backdoor from the CSP setting to the Valued CSP setting (VCSP, for short). This provides a means for augmenting a class of tractable VCSP instances to instances that are outside the class but of small distance to the class, where the distance is measured in terms of the size of a smallest backdoor. We establish that VCSP is fixed-parameter tractable when parameterized by the size of a smallest backdoor into every tractable class of VCSP instances characterized by a (possibly infinite) tractable valued constraint language of finite arity and finite domain. We further extend this fixed-parameter tractability result to so-called “scattered classes” of VCSP instances where each connected component may belong to a different tractable class.

The authors acknowledge support by the Austrian Science Fund (FWF, project P26696). Robert Ganian is also affiliated with FI MU, Brno, Czech Republic.

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Notes

  1. 1.

    The literature also defines the notion of tractability [17, 19], which we do not consider here. We remark that, to the best of our knowledge, all known tractable constraint languages are also globally tractable [17, 19].

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Authors and Affiliations

  1. Algorithms and Complexity Group, TU Wien, Vienna, Austria

    Robert Ganian, M. S. Ramanujan & Stefan Szeider

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  1. Robert Ganian
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  2. M. S. Ramanujan
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  3. Stefan Szeider
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Correspondence to Stefan Szeider .

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

    Michel Rueher

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Ganian, R., Ramanujan, M.S., Szeider, S. (2016). Backdoors to Tractable Valued CSP. 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_16

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  • DOI: https://doi.org/10.1007/978-3-319-44953-1_16

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