An arc-consistency algorithm optimal in the number of constraint checks

C. Bessiere and M.O. Cordier (1994) said that the AC-6 arc consistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are bidirectional. None of the previous algorithms achieving arc-consistency (AC-3, AC-4, AC-6) use constraint bidirectionality. We propose here an improved version of AC-6 which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed (i.e. given a variable, value, and arc ordering, it performs the minimum possible number of constraint checks according to these orders)