Theoretical analysis of singleton arc consistency and its extensions

Singleton arc consistency (SAC) is a consistency property that is simple to specify and is stronger than arc consistency. Algorithms have already been proposed to enforce SAC, but they have a high time complexity. In this paper, we give a lower bound to the worst-case time complexity of enforcing SAC on binary constraints. We discuss two interesting features of SAC. The first feature leads us to propose an algorithm for SAC that has optimal time complexity when restricted to binary constraints. The second feature leads us to extend SAC to a stronger level of local consistency that we call Bidirectional SAC (BiSAC). We also show the relationship between SAC and the propagation of disjunctive constraints.