A Compression Algorithm for Large Arity Extensional Constraints

We present an algorithm for compressing table constraints representing allowed or disallowed tuples. This type of constraint is used for example in configuration problems, where the satisfying tuples are read from a database. The arity of these constraints may be large. A generic GAC algorithm for such a constraint requires time exponential in the arity of the constraint to maintain GAC, but Bessiere and Regin showed in [1] that for the case of allowed tuples, GAC can be enforced in time proportional to the number of allowed tuples, using the algorithm GAC-Schema. We introduce a more compact representation for a set of tuples, which allows a potentially exponential reduction in the space needed to represent the satisfying tuples and exponential reduction in the time needed to enforce GAC. We show that this representation can be constructed from a decision tree that represents the original tuples and demonstrate that it does in practice produce a significantly shorter description of the constraint. We also show that this representation can be efficiently used in existing algorithms and can be used to improve GAC-Schema further. Finally, we show that this method can be used to improve the complexity of enforcing GAC on a table constraint defined in terms of forbidden tuples.