# Directional arc consistency

An ordering is associated to the variables in the constraint network and constraints are made arc consistent only in in the direction of the ordering. For instance, if $LaTeX: x_i \le_{order} x_j$ and constraint $LaTeX: c_{ij}$ exists, directional arc consistency enforces that each value in the domain of $LaTeX: x_i$ is consistent with at least one value in the domain of $LaTeX: x_j$ but not necessarily the other way around.