Making Bound Consistency as Effective as Arc Consistency

We study under what conditions bound consistency (BC) and arc consistency  (AC),  two forms of propagation used in constraint solvers, are equivalent to each other. We show that they prune exactly the same values when the propagated constraint is connected row convex / closed under median and its complement is row convex. This  characterization is exact for binary constraints. Since row convexity depends on the order of the values in the domains, we give polynomial algorithms for computing orders under which BC and AC are equivalent, if any.