A test for tractability

  • Peter Jeavons
  • David Cohen
  • Marc Gyssens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1118)


Many combinatorial search problems can be expressed as ‘constraint satisfaction problems’, and this class of problems is known to be NP-complete in general. In this paper we investigate restricted classes of constraints which give rise to tractable problems. We show that any set of constraints must satisfy a certain type of algebraic closure condition in order to avoid NP-completeness. We also describe a simple test which can be applied to establish whether a given set of constraints satisfies a condition of this kind. The test involves solving a particular constraint satisfaction problem, which we call an ‘indicator problem’.


Constraint satisfaction problem complexity NP-completeness indicator problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Jeavons
    • 1
  • David Cohen
    • 1
  • Marc Gyssens
    • 2
  1. 1.Department of Computer Science, Royal HollowayUniversity of LondonUK
  2. 2.Department WNIUniversity of LimburgDiepenbeekBelgium

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