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.

中文翻译：

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邻居单例一致性

CP求解器主要使用弧一致性（AC）作为二进制约束的默认传播方法。存在许多更强的一致性，例如三角形一致性（例如RPC和maxRPC），但是尽管结果表明它们在许多问题上都优于AC，但它们的使用受到限制。这是由于将它们合并到求解器中所涉及的复杂性。另一方面，单例一致性（例如SAC）可以很容易地制作为求解器，但是在实践中它们太昂贵了。为了在三角一致性的效率和单例实现的简便性之间寻求平衡，我们研究了邻域单项一致性的族。（NSC）扩展了最近提出的邻域SAC（NSAC）。我们提出了这个家族的几个新成员，并在理论和实验上对其进行了研究。我们的理论结果表明，提出的NSC的修剪能力介于RPC和（3,1）一致性之间。使用非常简单的算法来实现NSC，我们证明了NSC系列的某些成员作为针对二进制约束的通用传播方法具有相当的竞争力，在某些问题类别上明显优于现有的传播技术。