Huang Lie Jun edited on_constraint_graph_begin_quote__.tex  about 8 years ago

Commit id: c2f2e825072002c87e0d2880b9c61bce1c41fd64

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On constraint graph:  \begin{quote}  The nodes of the graph correspond to variables of the problem, and a link connects any two variables that participate in a constraint.  \end{quote}  Assuming that we have no other arcs to process, the following is the constraint graph constructed:  \node A  \node B  \node C  \((A, B)\)  Since \(A = B + 1\) is the constraint, Domain \(D_A\) will be reduced to \{1, 2, 3, 4\} to be make arc \((A, B)\) arc-consistent.  State:  \(D_A = \{1, 2, 3, 4\}\)  \(D_B = \{0, 1, 2, 3, 4\}\)  \(D_C = \{0, 1, 2, 3, 4\}\)  \subsection{. \((B, A)\)}  Since \(B = A - 1\) is the constraint, Domain \(D_B\) will be reduced to \{0, 1, 2, 3\} to be make arc \((B, A)\) arc-consistent.  State:  \(D_A = \{1, 2, 3, 4\}\)  \(D_B = \{0, 1, 2, 3\}\)  \(D_C = \{0, 1, 2, 3, 4\}\)  \subsection{. \((B, C)\)}  Since \(B = 2C\) is the constraint, Domain \(D_B\) will be reduced to \{0, 2\} to be make arc \((B, C)\) arc-consistent.  State:  \(D_A = \{1, 2, 3, 4\}\)  \(D_B = \{0, 2\}\)  \(D_C = \{0, 1, 2, 3, 4\}\)  \subsection{. \((C, B)\)}  Since \(C = \frac{B}{2}\) is the constraint, Domain \(D_C\) will be reduced to \{0, 1\} to be make arc \((C, B)\) arc-consistent.  State:  \(D_A = \{1, 2, 3, 4\}\)  \(D_B = \{0, 2\}\)  \(D_C = \{0, 1\}\)