As in Waltz filtering, constraint propagation can greatly reduce the size of a CSP search:
An arc (X, Y) is arc-consistent if for every value x &isin X, there is some value y &isin Y that satisfies the constraint represented by the arc. k-consistency follows multiple arcs to check for consistency (arc consistency is 2-consistency).
Some search may be left after constraint propagation, but the amount of search can be greatly reduced.
For scheduling problems, possible value sets can be represented as ranges [ min, max ]; constraints can allow the range limits to be reduced.
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