Consistency techniques proved to be an efficient method for reducing the search space of CSP and hence they were modified for soft constraint frameworks too. Several algorithms for local consistency in Weighted CSP, where costs are assigned to tuples, were introduced in [2,3]. The strongest form among them is Full Star Directional Arc Consistency (FDAC*). The algorithm for enforcing FDAC* is based on sending costs from one constraint to another in one direction with respect to the fixed order of variables.
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