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
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 the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP.
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 17155The contribution was presented at CP 2016 :http://cp2016.a4cp.org/ Abstract. Broken triangles constitute an important concept not only for solving constraint satisfaction problems in polynomial time, but also for variable elimination or domain reduction by merging domain values. Specifically, for a given variable in a binary arc-consistent CSP, if no broken triangle occurs on any pair of values, then this variable can be eliminated while preserving satisfiability. More recently, it has been shown that even when this rule cannot be applied, it could be possible that for a given pair of values no broken triangle occurs. In this case, we can apply a domain-reduction operation which consists in merging these values while preserving satisfiability.In this paper we show that under certain conditions, and even if there are some broken triangles on a pair of values, these values can be merged without changing the satisfiability of the instance. This allows us to define a stronger merging operation and a new tractable class of binary CSP instances. We report experimental trials on benchmark instances.
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