Expected-Case Analysis for Delayed Filtering

Abstract

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.