Non-viability deductions in Arc-consistency computation

Arc-Consistency (AC) techniques have been used extensively in the study of Constraint Satisfaction Problems (CSP). These techniques are used to simplify the CSP before or during the search for its solutions. Some of the most efficient algorithms for AC computation are AC6++ and AC-7. The novelty of these algorithms is that they satisfy the so-called four desirable properties for AC computation. The main purpose of these interesting properties is to reduce as far as possible the number of constraint checks during AC computation while keeping a reasonable space complexity. In this paper we prove that, despite providing a remarkable reduction in the number of constraint checks, the four desirable properties do not guarantee a minimal number of constraint checks. We therefore refute the minimality claim in the paper introducing these properties. Furthermore, we propose a new desirable property for AC computation and extend AC6++ and AC-7 to consider such a property. We show theoretically and experimentally that the new property provides a further substantial reduction in the number of constraint checks.