Expected-Case Analysis for Delayed Filtering
One way to address the tradeoff between the efficiency and the effectiveness of filtering algorithms for global constraints is as follows: Instead of compromising on the level of consistency, compromise on the frequency at which arc consistency is enforced during the search. In this paper, a method is suggested to determine a reasonable filtering frequency for a given constraint.
For dense instances of AllDifferent and its generalization, the Global Cardinality Constraint, let n and m be, respectively, the number of nodes and edges in the variable-value graph. Under the assumption that propagation is random (i.e., each edge removed from the variable-value graph is selected at random), it is shown that recomputing arc consistency only after Θ(m/n) edges were removed results in a speedup while, in the expected sense, filtering effectiveness is comparable to that of enforcing arc consistency at each search step.
KeywordsGlobal Constraint Residual Graph AllDifferent Constraint Dense Instance Danish National Research Foundation
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