As in Waltz filtering, constraint propagation can greatly reduce the size of a CSP search:

• Initialize nodes to sets of all values in their respective domains.

• When the possible values of a node constrain the possible values of its neighbors, remove impossible values from the sets for the neighbors.

  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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