Ways of Maintaining Arc Consistency in Search Using the Cartesian Representation

The search space of constraint satisfaction problems (CSPs) can be reduced by using value interchangeability. This notion consists of aggregating subsets of values that behave similarly on the future branches of the search. BT-CPR [8], is a typical backtracking algorithm using value interchangeability. It uses the Cartesian product representation of the search space (CPR) which aggregates partial solutions and proves particularly useful for finding and representing all solutions of a CSP. It is assessed that maintaining arc-consistency (MAC) is the most efficient general algorithm for solving hard problems. A few work on combining MAC with CPR exists. In this paper we study comparatively two other possible alternatives of MAC-CPR.