Neighborhood Inverse Consistency Preprocessing

Eugene C. Freuder, Charles D. Elfe

Constraint satisfaction consistency preprocessing methods are used to reduce search effort. Time and especially space costs limit the amount of preprocessing that will be cost effective. A new form of consistency preprocessing, neighborhood inverse consistency, can achieve more problem pruning than the usual arc consistency preprocessing in a cost effective manner. There are two basic ideas: 1) Common forms of consistency enforcement basically operate by identifying and remembering solutions to subproblems for which a consistent value cannot be found for some additional problem variable. The space required for this memory can quickly become prohibitive. Inverse consistency basically operates by removing values for variables that are not consistent with any solution to some subproblem involving additional variables. The space requirement is at worst linear. 2) Typically consistency preprocessing achieves some level of consistency uniformly throughout the problem. A subproblem solution will be tested against each additional variable that constrains any subproblem variable. Neighborhood consistency focuses attention on the subproblem formed by the variables that are all constrained by the value in question. By targeting highly relevant subproblems we hope to "shim the cream", obtaining a high payoff for a limited cost.


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