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\subsection{On arc-consistency:}  On arc-consistency:  \begin{quote} \(X_{i}\) is arc-consistent with respect to another variable \(X_{j}\) if for every value in the current domain \(D_{i}\) there is some value in the domain \(D_{j}\) that satisfies the binary constraint on the arc (\(X_{i}, X_{j}\)) \end{quote}