Filtering by Generalized Arc Consistency (GAC) is a fundamental technique in Constraint Programming. Recent advances in GAC algorithms for extensional constraints rely on direct manipulation of tables during search. Simple Tabular Reduction (STR), which systematically removes invalid tuples from tables, has been shown to be a simple yet efficient approach. STR2, a refinement of STR, is considered to be among the best filtering algorithms for positive table constraints. In this paper, we introduce a new GAC algorithm called STR3 that is specifically designed to enforce GAC during search. STR3 can completely avoid unnecessary traversal of tables, making it optimal along any path of the search tree. Our experiments show that STR3 is much faster than STR2 when the average size of the tables is not reduced drastically during search.
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