解释AllDifferent约束的合取
Propagating Conjunctions of AllDifferent Constraints
摘要：
我们研究了两个AllDifferent约束的结合的传播算法。AllDifferent约束的解可以看作是变量/值二分图上的完美匹配。因此，我们调查的问题，发现同时二部匹配。我们提出了一个著名的霍尔定理的扩展，其特点是同时存在的二分匹配。不幸的是，找到这样的匹配一般是NP困难的。然而，我们证明了一个令人惊讶的结果，找到一个同时匹配的凸二分图只需要多项式时间。基于这个理论结果，我们给出了第一个求解两个AllDifferent约束合取问题的多项式时间界一致性算法。我们确定了一个病态的问题上，这个传播是指数速度比现有的传播。我们的实验表明，这种新的传播器可以提供显着的好处比现有的方法。
英文摘要：
We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two AllDifferent constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.
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