## Abstract

CP solvers predominantly use arc consistency (AC) as the default propagation method for binary constraints. Many stronger consistencies, such as triangle consistencies (e.g. RPC and maxRPC) exist, but their use is limited despite results showing that they outperform AC on many problems. This is due to the intricacies involved in incorporating them into solvers. On the other hand, singleton consistencies such as SAC can be easily crafted into solvers but they are too expensive in practice. Seeking a balance between the efficiency of triangle consistencies and the ease of implementation of singleton ones, we study the family of *neighborhood singleton consistencies* (NSCs) which extends the recently proposed neighborhood SAC (NSAC). We propose several new members of this family and study them both theoretically and experimentally. Our theroretical results show that the pruning power of the proposed NSCs ranges between that of RPC and (3,1)-consistency. Using a very simple algorithm for the implementation of NSCs, we demonstrate that certain members of the NSC family are quite competitive as general-purpose propagation methods for binary constraints, significantly outperforming the existing propagation techniques on some problem classes.

## Keywords

Constraint propagation Local consistency Singleton consistency## Notes

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