Extending arc-consistency algorithms for Non-Normalized CSPs

Abstract

Arc-consistency algorithms are widely used to prune the search space of CSPs. Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and they require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, that is, they cannot delete any value and they consume a lot of checks and time. In this paper, we present AC4-OP and AC3-NN, two extended versions of AC4 and AC3 respectively, for dealing with non-normalized CSPs. Furthermore AC4-OP is an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing for their later evaluation the inverse supports that are found. The use of AC4-OP reduces number of constraint checks by 50%. Also, the average of propagations is reduced by at least 15% while pruning the same search space as AC4.