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The Parameterized Complexity of Local Consistency

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Principles and Practice of Constraint Programming – CP 2011 (CP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6876))

Abstract

We investigate the parameterized complexity of deciding whether a constraint network is k-consistent. We show that, parameterized by k, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size d and the maximum number l of constraints in which a variable occurs. We show that parameterized by k + d, the problem drops down one complexity level and becomes co-W[1]-complete. Parameterized by k + d + l the problem drops down one more level and becomes fixed-parameter tractable. We further show that the same complexity classification applies to strong k-consistency, directional k-consistency, and strong directional k-consistency.

Our results establish a super-polynomial separation between input size and time complexity. Thus we strengthen the known lower bounds on time complexity of k-consistency that are based on input size.

This research was funded by the ERC (COMPLEX REASON, 239962).

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Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Serge Gaspers & Stefan Szeider

Authors
  1. Serge Gaspers
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  2. Stefan Szeider
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Editors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

    Jimmy Lee

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Gaspers, S., Szeider, S. (2011). The Parameterized Complexity of Local Consistency. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_24

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  • DOI: https://doi.org/10.1007/978-3-642-23786-7_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23785-0

  • Online ISBN: 978-3-642-23786-7

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