Restricted path consistency (RPC) is a strong local consistency for binary constraints that was proposed 20 years ago and was identified as a promising alternative to arc consistency (AC) in an early experimental study of local consistencies for binary constraints. However, in contrast to other strong local consistencies such as singleton arc consistency (SAC) and max restricted path consistency (maxRPC), it has been neglected since then. In this paper we revisit RPC. First we propose RPC3, a new RPC algorithm that is very easy to implement and can be efficiently applied throughout search. Then we perform a wide experimental study of RPC3 and a light version that achieves an approximation of RPC, comparing them to state-of-the-art AC and maxRPC algorithms. Experimental results obtained under various solver settings, regarding the branching scheme, the variable ordering heuristic, and restarts, clearly show that light RPC is by far more efficient than both AC and maxRPC when applied throughout search. We also examine the experimental behaviour of an algorithm for a simple extension of RCP called 2-RPC, showing that it is competitive with RPC3, and better than both AC and maxRPC. Overall, our results strongly suggest that it is time to reconsider the established perception that MAC is the best general purpose method for solving binary CSPs.

中文翻译：

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重访受限路径一致性

限制路径一致性（RPC）是20年前提出的针对二进制约束的强局部一致性，在对二进制约束的局部一致性的早期实验研究中，它被确定为弧形一致性（AC）的有希望的替代方法。但是，与其他强大的局部一致性（例如单例弧一致性（SAC）和最大受限路径一致性（maxRPC））相比，此后就被忽略了。在本文中，我们将回顾RPC。首先，我们提出RPC3，这是一种新的RPC算法，它非常易于实现，并且可以有效地应用于整个搜索。然后，我们对RPC3和一个轻型版本进行了广泛的实验研究，该版本可以近似RPC，并将它们与最新的AC和maxRPC算法进行比较。在各种求解器设置下获得的有关分支方案的实验结果，变量排序试探法并重新启动，清楚地表明，轻量级RPC在整个搜索中应用时，其效率远比AC和maxRPC高。我们还研究了一种简单的RCP扩展（称为2-RPC）算法的实验行为，表明该算法与RPC3竞争，并且比AC和maxRPC都好。总体而言，我们的结果强烈表明，现在应该重新考虑已建立的认识，即MAC是解决二进制CSP的最佳通用方法。