Local Consistency

In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints. Several such conditions exist, the most known being node consistency, arc consistency, and path consistency. Local consistency can be enforced via transformations of the problem called constraint propagation.

Local consistency conditions can be grouped into various classes. The original local consistency conditions require that every consistent assignment can be consistently extended to another variable. Directional consistency only requires this condition to be satisfied when the other variable is higher than the ones in the assignment, according to a given order. Relational consistency includes extensions to more than one variable, but this extension is only required to satisfy a given constraint or set of constraints.

Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions. Such a transformation is called constraint propagation. Constraint propagation works by reducing domains of variables, strengthening constraints, or creating new ones. This leads to a reduction of the search space, making the problem easier to solve by some algorithms. Constraint propagation can also be used as an unsatisfiability checker, incomplete in general but complete in some particular cases.