  Among the local consistency techniques used for solving constraint networks,
path-consistency (PC) has received a great deal of attention. However,
enforcing PC is computationally expensive and sometimes even unnecessary.
Directional path-consistency (DPC) is a weaker notion of PC that considers a
given variable ordering and can thus be enforced more efficiently than PC. This
paper shows that DPC (the DPC enforcing algorithm of Dechter and Pearl) decides
the constraint satisfaction problem (CSP) of a constraint language if it is
complete and has the variable elimination property (VEP). However, we also show
that no complete VEP constraint language can have a domain with more than 2
values. We then present a simple variant of the DPC algorithm, called DPC*, and
show that the CSP of a constraint language can be decided by DPC* if it is
closed under a majority operation. In fact, DPC* is sufficient for guaranteeing
backtrack-free search for such constraint networks. Examples of majority-closed
constraint classes include the classes of connected row-convex (CRC)
constraints and tree-preserving constraints, which have found applications in
various domains, such as scene labeling, temporal reasoning, geometric
reasoning, and logical filtering. Our experimental evaluations show that DPC*
significantly outperforms the state-of-the-art algorithms for solving
majority-closed constraints.
