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On the Power of k-Consistency

  • Albert Atserias
  • Andrei Bulatov
  • Victor Dalmau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

The k-consistency algorithm for constraint-satisfaction problems proceeds, roughly, by finding all partial solutions on at most k variables and iteratively deleting those that cannot be extended to a partial solution by one more variable. It is known that if the core of the structure encoding the scopes of the constraints has treewidth at most k, then the k-consistency algorithm is always correct. We prove the exact converse to this: if the core of the structure encoding the scopes of the constraints does not have treewidth at most k, then the k-consistency algorithm is not always correct. This characterizes the exact power of the k-consistency algorithm in structural terms.

Keywords

Polynomial Time Relational Structure Partial Solution Constraint Satisfaction Tree Decomposition 
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 2007

Authors and Affiliations

  • Albert Atserias
    • 1
  • Andrei Bulatov
    • 2
  • Victor Dalmau
    • 3
  1. 1.Universitat Politècnica de Catalunya, BarcelonaSpain
  2. 2.Simon Fraser University, VancouverCanada
  3. 3.Universitat Pompeu Fabra, BarcelonaSpain

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