Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for non-binary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in non-binary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worst-case complexities of the resulting algorithms. Finally, we make a preliminary empirical study.
An empirical study of phase transitions in binary constraint satisfaction problems
