The Alldifferent Constraint: Exploiting Strongly-connected Components and Other Efficiency Measures

The AllDifferent constraint is a crucial component of any constraint toolkit, language or solver, since it is very widely used in a variety of constraint models. The literature contains many different versions of this constraint, which trade strength of inference against computational cost. In this paper, we focus on the highest strength of inference (enforcing a property known as generalised arc consistency GAC), and propose several new variants of the AllDifferent constraint propagation algorithm that achieve this. Most importantly, we improve incrementality by exploiting the strongly-connected components discovered during the standard propagation process, and improve efficiency by triggering the propagation process less often. We perform an extensive empirical evaluation of the new variants of AllDifferent versus existing GAC algorithms, as well as a fast AllDifferent algorithm that does less propagation. The results confirm the value of our new variants, which can improve run-times over the state-of-the-art by over five times.