Compiling and Executing Disjunctions of Finite Domain Constraints Compiling and Executing Disjunctions of Finite Domain Constraints

We present two schemes for compiling disjunctions of nite domain constraints, where disjunction is treated as constructive. In the rst scheme each disjunction is compiled to a set of indexicals, i.e. a set of range functions computing domain restrictions, such that the evaluation of the indexicals maintains a weak form of consistency of the disjunction. The second scheme is based on constraint lifting, i.e. constructive disjunction applied to the set of constraint stores given by executing a disjunction of goals, for which we provide an algorithm for lifting nite domain constraints. This scheme maintains stronger consistency than the rst with a penalty in eeciency. We compare the two schemes with speculative disjunction, i.e. disjunction executed nondeterministically, and with disjunction via cardinality. Our conclusions are that the indexical scheme implements the most eecient pruning for many disjunctive constraints, such as resource and max-imum/minimum constraints, and that the lifting scheme can be used for implementing lookahead pruning. Abstract We present two schemes for compiling disjunctions of nite domain constraints, where disjunction is treated as constructive. In the rst scheme each disjunction is compiled to a set of indexicals, i.e. a set of range functions computing domain restrictions, such that the evaluation of the indexicals maintains a weak form of consistency of the disjunction. The second scheme is based on constraint lifting, i.e. constructive disjunc-tion applied to the set of constraint stores given by executing a disjunction of goals, for which we provide an algorithm for lifting nite domain constraints. This scheme maintains stronger consistency than the rst with a penalty in eeciency. We compare the two schemes with speculative disjunc-tion, i.e. disjunction executed nondeterministically, and with disjunction via cardinality. Our conclusions are that the indexical scheme implements the most eecient pruning for many disjunctive constraints, such as resource and maximum/minimum constraints, and that the lifting scheme can be used for implementing lookahead pruning.