In a minimal binary constraint network, every tuple of a constraint relation can be extended to a solution. It was conjectured that computing a solution to such a network is NP hard. We prove this conjecture. We also prove a conjecture by Dechter and Pearl stating that for k ≥ 2 it is NP-hard to decide whether a constraint network can be decomposed into an equivalent k-ary constraint network, and study related questions.


Polynomial Time Constraint Satisfaction Problem Single Solution Propositional Variable Constraint Network 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Georg Gottlob
    • 1
  1. 1.Computer Science Department and Oxford Man InstituteUniversity of OxfordOxfordUK

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