Broken Triangles Revisited

Martin Cooper (1, 2) , Aymeric Duchein (1) , Guillaume Escamocher (3)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 UT3 - Université Toulouse III - Paul Sabatier
3 INSIGHT - Insight Centre for Data Analytics

A broken triangle is a pattern of (in)compatibilities between assignments in a binary CSP (constraint satisfaction problem). In the absence of certain broken triangles, satisfiability-preserving domain reductions are possible via merging of domain values. We investigate the possibility of maximising the number of domain reduction operations by the choice of the order in which they are applied, as well as their interaction with arc consistency operations. It turns out that it is NP-hard to choose the best order.

Keywords: Constraint satisfaction problem; CSP; Broken-triangle merging; Complexity; NP-complete

Domains: Artificial Intelligence [cs.AI]; Machine Learning [cs.LG]; Logic in Computer Science [cs.LO]; Computation and Language [cs.CL]

Martin Cooper, Aymeric Duchein, Guillaume Escamocher. Broken Triangles Revisited. 21st International Conference on Principles and Practice of Constraint Programming (CP 2015), Aug 2015, Cork, Ireland. pp. 58-73. ⟨hal-01343049⟩