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.
KeywordsValued Constraint Satisfaction Problem Value merging Value elimination Tractability
We would like to thank Wady Naanaa for useful discussion concerning the generalisation to the general-arity case.
- 9.Freuder, E.C.: Eliminating interchangeable values in constraint satisfaction problems. In: Dean, T.L., McKeown, K. (eds.) Proceedings of the 9th National Conference on Artificial Intelligence, Anaheim, CA, USA, 14–19 July 1991, vol. 1, pp. 227–233. AAAI Press/The MIT Press (1991)Google Scholar
- 11.Gent, I.P., Petrie, K.E., Puget, J.F.: Symmetry in constraint programming. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, Foundations of Artificial Intelligence, vol. 2, pp. 329–376. Elsevier (2006)Google Scholar
- 15.van Hoeve, W.J., Katriel, I.: Global constraints. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, Foundations of Artificial Intelligence, vol. 2, pp. 169–208. Elsevier (2006)Google Scholar
- 19.Roney-Dougal, C.M., Gent, I.P., Kelsey, T., Linton, S.: Tractable symmetry breaking using restricted search trees. In: Proceedings of the 16th European Conference on Artificial Intelligence, ECAI 2004, pp. 211–215 (2004)Google Scholar