Light Algorithms for Maintaining Max-RPC During Search

This article presents two new algorithms whose purpose is to maintain the Max-RPC domain filtering consistency during search with a minimal memory footprint and implementation effort. Both are sub-optimal algorithms that make use of support residues, a backtrack-stable and highly efficient data structure which was successfully used to develop the state-of-the-art AC-3rm algorithm. The two proposed algorithms, Max-RPCrm and L-Max-RPCrm are competitive with best, optimal Max-RPC algorithms, while being considerably simpler to implement. L-Max-RPCrm computes an approximation of the Max-RPC consistency, which is guaranteed to be strictly stronger than AC with the same space complexity and better worst-case time complexity than Max-RPCrm. In practice, the difference in filtering power between L-Max-RPCrm and standard Max-RPC is nearly indistinguishable on random problems. Max-RPCrm and L-Max-RPCrm are implemented into the Choco Constraint Solver through a strong consistency global constraint. This work opens new perspectives upon the development of strong consistency algorithms into constraint solvers.