Arc consistency
= 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.