Improving the Performance of Consistency Algorithms by Localizing and Bolstering Propagation in a Tree Decomposition

摘要

The tractability of a Constraint Satisfaction Problem (CSP) is guaranteed by a direct relationship between its consistency level and a structural parameter of its constraint network such as the treewidth. This result is not widely exploited in practice because enforcing higher-level consistencies can be costly and can change the structure of the constraint network and increase its width. Recently, R(*,m)C was proposed as a relational consistency property that does not modify the structure of the graph and, thus, does not affect its width. In this paper, we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcing R(*,m)C and getting closer to the above tractability condition. Those strategies are: a) localizing the application of the consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation between clusters by adding redundant constraints at their separators, for which we propose three new schemes. We characterize the resulting consistency properties by comparing them, theoretically and empirically, to the original R(*,m)C and the popular GAC and maxRPWC, and establish the benefits of our approach for solving difficult problems.