Using Constraints with Memory to Implement Variable Elimination

Adaptive consistency is a solving algorithm for constraint networks. Its basic step is variable elimination: it takes a network as input, and produces an equivalent network with one less variable and one new constraint (the join of the variable bucket). This process is iterated until every variable is eliminated, and then all solutions can be computed without backtracking. A direct, naive implementation of variable elimination may use more space than needed, which renders the algorithm inapplicable in many cases. We present a more sophisticated implementation, based on the projection with memory of constraints. When a variable is projected out from a constraint, we keep the supports which that variable gave to the remaining tuples. Using this data structure, we compute a set of new factorized constraints, equivalent to the new constraint computed as the join of the variable bucket, but using less space for a wide range of problems. We provide experimental evidence of the benefits of our approach.