Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems

Martin Cooper (1, 2) , Aymeric Duchein (1) , Achref El Mouelhi (3, 4) , Guillaume Escamocher (5) , Cyril Terrioux (3, 4) , Bruno Zanuttini (6)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 UT3 - Université Toulouse III - Paul Sabatier
3 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
4 COALA - COntraintes, ALgorithmes et Applications
5 Insight Centre for Data Analytics
6 Equipe MAD - Laboratoire GREYC - UMR6072

A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in arbitrary instances of binary CSP, thus providing a novel polynomial-time reduction operation. Extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity and we investigate the theoretical relationship with resolution in SAT. A directional version of general-arity BTP-merging then allows us to extend the BTP tractable class previously defined only for binary CSP. We investigate the complexity of several related problems including the recognition problem for the general-arity BTP class when the variable order is unknown, finding an optimal order in which to apply BTP merges and detecting BTP-merges in the presence of global constraints such as AllDifferent.

Mots clés: CSP; domain reduction; constraint satisfaction; tractable class; hybrid tractability; NP-completeness; global constraints

Domaines: Informatique [cs]; Intelligence artificielle [cs.AI]; Complexité [cs.CC]; Logique en informatique [cs.LO]

Martin Cooper, Aymeric Duchein, Achref El Mouelhi, Guillaume Escamocher, Cyril Terrioux, et al.. Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems. Artificial Intelligence, 2016, 234, pp.196-218. ⟨10.1016/j.artint.2016.02.001⟩. ⟨hal-01356091⟩