From Restricted Path Consistency to Max-Restricted Path Consistency

There is no need to show the importance of the filtering techniques to solve constraint satisfaction problems i.e. to find values for problem variables subject to constraints that specify which combinations of values are consistent. They can be used during a preprocessing step to remove once and for all some local inconsistencies, or during the search to efficiently prune the search tree. Recently, in [5], a comparison of the most practicable filtering techniques concludes that restricted path consistency (RPC) is a promising local consistency that requires little additional cpu time compared to arc consistency while removing most of the path inverse inconsistent values. However, the RPC algorithm used for this comparison (presented in [1] and called RPC1 in the following) has a non optimal worst case time complexity and bad average time and space complexities. Therefore, we propose RPC2, a new RPC algorithm with O(end2) worst case time complexity and requiring less space than RPC1 in practice. The second aim of this paper is to extend RPC to new local consistencies, k-RPC and Max-RPC, and to compare their pruning efficiency with the other practicable local consistencies. Furthermore, we propose and study a Max-RPC algorithm based on AC-6 that we used for this comparison.