Domain reduction is an essential tool for solving the constraint satisfaction problem (CSP). In the binary CSP, neighbourhood substitution consists in eliminating a value if there exists another value which can be substituted for it in each constraint. We show that the notion of neighbourhood substitution can be strengthened in two distinct ways without increasing time complexity. We also show the theoretical result that, unlike neighbourhood substitution, finding an optimal sequence of these new operations is NP-hard.

中文翻译：

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加强邻里替代

域缩减是解决约束满足问题 (CSP) 的重要工具。在二元 CSP 中，邻域替换包括消除一个值，如果在每个约束中存在另一个可以替换它的值。我们表明，邻域替代的概念可以通过两种不同的方式得到加强，而不会增加时间复杂度。我们还展示了理论结果，与邻域替换不同，找到这些新操作的最佳序列是 NP 难的。