Improving efficiency in Constraint Logic Programming through constraint modeling with rules and hypergraphs

Constraint Satisfaction Problems typically exhibit very strong combinatorial explosion of exponential nature. This is due to their intrinsic nature: a number of variables have to be assigned values from their domains. This induces a very large number of potential solutions to be explored. Most typical approaches are oriented towards reduction of the inevitable search through advanced constraint propagation methods. In this paper we analyze a possibility of improving efficiency in Constraint Logic Programming. A hypergraph model of constraints is proposed as a base tool for planning approach. Building the partial solution plan in the form of definite sequence of variables is performed a priori. The plan is executed with a classical backtrack search. The whole process is focused on efficient use of variable values propagation rules. Two example cryptoarithmetic problems are explored in order to explain the proposed approach. The reported results are amazing in comparison to contemporary tools.