The Parameterized Complexity of Local Consistency

  • Serge Gaspers
  • Stefan Szeider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6876)


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.


Parameterized Complexity Parameterized Problem Input Size Constraint Network Constraint Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Serge Gaspers
    • 1
  • Stefan Szeider
    • 1
  1. 1.Institute of Information SystemsVienna University of TechnologyViennaAustria

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