How does arc consistency work?
Arc Consistency is based on the concept of a graph where every variable creates a node in the graph and the constraints create arcs that connect the nodes. For example, variables X and Y would create two corresponding nodes in the graph. A constraint X + Y = 10 would create two arcs in the graph. The first arc based on the constraint is X = 10 – Y. This arc would be drawn from Y, the source, to X, the target. Similarly, a second arc, Y = X – 10, would be drawn from X to Y. The arcs indicate the dependencies between the nodes and can be traversed by an algorithm to ensure that all nodes are ‘consistent’ with each other. When a variable is defined, the possible values that may be assigned to the variable are declared as well. For instance, X may be assigned a value between 1 and 10. When values are removed from a variable / node, the arcs originating from the node can be used to remove values from nodes targeted by the arcs. As other nodes are changed, they will propagate changes to othe
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