Consistency enforcement is used to prune the search tree of a constraint satisfaction problem (CSP). Arc consistency (AC) is a well‐studied consistency level, with many implementations. Bounds consistency (BC), a looser consistency level, is known to have equal time complexity to AC. To solve a CSP, we have to implement an algorithm of our own or employ an existing solver. In any case, at some point, we have to decide between enforcing either AC or BC. As the choice between AC or BC is more or less predefined and currently made without considering the individualities of each CSP, this study attempts to make this decision deterministic and efficient, without the need of trial and error. We find that BC fits better while solving a CSP with its maximum domains' size being greater than its constrained variables number. We study the behavior of maintaining arc or bounds consistency during search, and we show how the overall search methods complexity is affected by the employed consistency level.

中文翻译：

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圆弧和边界一致性之间的困境

一致性强制用于修剪约束满足问题（CSP）的搜索树。电弧一致性（AC）是经过充分研究的一致性级别，具有许多实现方式。边界一致性（BC）是较宽松的一致性级别，已知与AC具有相同的时间复杂度。要求解CSP，我们必须实现自己的算法或使用现有的求解器。无论如何，在任何时候，我们都必须在执行AC还是BC之间做出决定。由于AC或BC之间的选择或多或少是预先确定的，并且当前是在不考虑每个CSP的个性的情况下进行的，因此本研究试图在无需反复试验的情况下，使该决策具有确定性和效率。我们发现，在求解CSP时，BC最适合，其最大域的大小大于其受约束变量的数量。我们研究行为在搜索过程中保持弧度或边界一致性，并且我们展示了所采用的一致性级别如何影响整体搜索方法的复杂性。