We define the Same and UsedBy constraints. UsedBy takes two sets of variables X and Z such that |X| ≥ |Z| and assigns values to them such that the multiset of values assigned to the variables in Z is contained in the multiset of values assigned to the variables in X. Same is the special case of UsedBy in which |X|=|Z|. In this paper we show algorithms that achieve arc consistency and bound consistency for the Same constraint and in its extended version we generalize them for the UsedBy constraint.


Single Edge Variable Node Parity Match Residual Graph Consistency Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Irit Katriel
    • 2
  • Sven Thiel
    • 2
  1. 1.Ecole des Mines de NantesNantesFrance
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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