A simple algebraic property is described which characterises all possible constraint types for which strong k-consistency is sufficient to ensure global consistency, for each k > 2.Expand

This paper extends the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously and shows that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming.Expand

It is shown that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms and the notion of multimorphism is used to give a complete classification of complexity for the Boolean case which extends several earlier classification results for particular special cases.Expand

A restricted set of contraints is identified which gives rise to a class of tractable problems which generalizes the notion of a Horn formula in propositional logic to larger domain sizes, and it is proved that the class of problems generated by any larger set of constraints is NP-complete.Expand

The broken-triangle property is introduced, which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure and can be detected in polynomial time.Expand

It is shown that an ordered version of arc consistency exists for all FCSPs with a strictly monotonic aggregation operator, and that it can be established by an algorithm whose worst-case complexity is identical to that of the optimal arc consistency algorithm for CSPs.Expand

Virtual Arc Consistency (VAC) is introduced which iteratively identifies and applies sequences of cost propagation over rational costs that are guaranteed to transform a WCSP in another WCSP with an improved constant cost.Expand

A set of constraints is identified which gives rise to a class of tractable problems and given polynomial time algorithms for solving such problems, and it is proved that the class of problems generated by any set of constraint not contained in this restricted set is NP-complete.Expand

A relaxed variant of soft arc consistency using rational costs is introduced, and for finite rational costs, the associated lower bound is shown to provide an optimal arc consistent reformulation of the initial problem.Expand