Integrating Constraint Propagation in Complete Solving of Linear Diophantine Systems

Several complete methods for solving linear Diophantine constraints have been proposed. They can handle infinite domains, but their pruning during search is relatively weak. In contrast to those, consistency techniques based constraint propagation provides stronger pruning and have been applied successfully to many combinatorial problems, but are limited to finite domains. This paper studies the combination of (1) a complete solver which is based on a geometric interpretation and (2) propagation techniques. We study the pruning potential created through such a combination, both conceptually and experimentally. In addition, it turns out that dynamic variables orderings can be easily embedded in the method. Our result is an extended solver, which is implemented in Java, based on which we present some interesting features and a few experimental results.