A Portfolio Approach for Enforcing Minimality in a Tree Decomposition

Minimality, a highly desirable consistency property of Constraint Satisfaction Problems (CSPs), is in general too expensive to enforce. Previous work has shown the practical benefits of restricting minimality to the clusters of a tree decomposition, allowing us to solve many difficult problems in a backtrack-free manner. We explore two alternative algorithms for enforcing minimality whose performance widely vary from one instance to another. We advocate a fine-grain portfolio approach to dynamically choose, during lookahead, the most appropriate algorithm for a cluster. Our strategy operates by selecting among two algorithms for enforcing minimality and an algorithm that enforces the lowest-level of consistency, which, in our setting, is Generalized Arc Consistency. Empirical evaluation on benchmark problems shows a significant improvement both in terms of the number of instances solved and CPU time.