Domain Reduction for Valued Constraints by Generalising Methods from CSP

For classical CSPs, the absence of broken triangles on a pair of values allows the merging of these values without changing the satisfiability of the instance, giving experimentally verified reduction in search time. We generalise the notion of broken triangles to VCSPs to obtain a tractable value-merging rule which preserves the cost of a solution. We then strengthen this value merging rule by using soft arc consistency to remove soft broken triangles and we show that the combined rule generalises known notions of domain value substitutability and interchangeability. Unfortunately the combined rules are no longer tractable to apply, but can still have applications as heuristics for reducing the search space.
Finally we consider the generalisation of another value-elimination rule for CSPs to binary VCSPs. This new rule properly generalises neighbourhood substitutability and so we expect it will also have practical applications.