The constrainedness of Arc consistency

  • Ian P. Gent
  • Ewan MacIntyre
  • Patrick Prosser
  • Paul Shaw
  • Toby Walsh
Session 5b
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)


We show that the same methodology used to study phase transition behaviour in NP-complete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NP-complete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NP-complete problems, constrainedness — and proxies for it which are cheaper to compute — can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ian P. Gent
    • 1
  • Ewan MacIntyre
    • 1
  • Patrick Prosser
    • 1
  • Paul Shaw
    • 1
  • Toby Walsh
    • 1
  1. 1.The APES Research Group, Department of Computer ScienceUniversity of StrathclydeGlasgowUK

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