Broken Triangles Revisited

International audienceA 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

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

International audienceA 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

Broken triangles revisited

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