Implementation of the Relation Domain for Constraint Programming

Relations are fundamental structures for knowledge representation. Relational queries are used to extract information from associated relations in databases. We propose to include relations in constraint programming (CP) as decision variables and promoting relational operations to constraints. That leads to new possibilities for modeling and solving CSPs. Performance and applicability are two aspects to take into account before considering the new domain practical. In this paper we address the problem of achieving a practical implementation of the system. That includes compact representation of the data in relations and good performance of the relational operations. This compact representation relies upon representing relations into binary decision diagrams (BDDs) and rewriting operations on relations for this specific representation. Optimized implementations of the operations exist when the BDD representation satisfies particular properties. A solver that maximizes the existence of such properties for a CSP on relations is provided. This ensures the maximum performance from the constraint solver. The implementation of the relation constraint system is publicly available as a Gecode extension[1].