Exploiting Multidirectionality in Coarse-Grained Arc Consistency Algorithms

Arc consistency plays a central role in solving Constraint Satisfaction Problems. This is the reason why many algorithms have been proposed to establish it. Recently, an algorithm called AC2001 and AC3.1 has been independently presented by their authors. This algorithm which is considered as a refinement of the basic algorithm AC3 has the advantage of being simple and competitive. However, it does not take into account constraint bidirectionality as AC7 does. In this paper, we address this issue, and, in particular, introduce two new algorithms called AC3.2 and AC3.3 which benefit from good properties of both AC3 and AC7. Indeed, AC3.2 and AC3.3 are as easy to implement as AC3 and take advantage of bidirectionality as AC7 does. More precisely, AC3.2 is a general algorithm which partially exploits bidirectionality whereas AC3.3 is a binary algorithm which fully exploits bidirectionality. It turns out that, when Maintaining Arc Consistency during search, MAC3.2, due to a memorization effect, is more efficient than MAC3.3 both in terms of constraint checks and cpu time. Compared to MAC2001/3.1, our experimental results show that MAC3.2 saves about 50% of constraint checks and, on average, 15% of cpu time.