 Arc consistency

A directed requirement for a binary constraint $R_{ij}$: every remaining $x\in D_i$ has at least one support $y\in D_j$ with $(x,y)\in R_{ij}$. Revising the arc $i\to j$ deletes unsupported values from $D_i$; it does not directly delete values from $D_j$. Full arc consistency requires the condition in both directions on every edge of the constraint graph. On general graphs, it need not imply that a complete solution exists.