From Restricted Path Consistency to Max-Restricted Path Consistency

There is no need to show the importance of the ltering tech niques to solve constraint satisfaction problems i e to nd 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 e ciently prune the search tree Recently in a comparison of the most practicable ltering techniques concludes that restricted path con sistency RPC is a promising local consistency that requires little ad ditional 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 and called RPC in the following has a non optimal worst case time complexity and bad average time and space complexities Therefore we propose RPC a new RPC algorithm with O end worst case time complexity and requiring less space than RPC 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 e ciency with the other practicable local consistencies Furthermore we propose and study a Max RPC algorithm based on AC that we used for this comparison