We present new filtering algorithms for Disjunctive and Cumulative constraints, each of which improves the complexity of the state-of-the-art algorithms by a factor of log n. We show how to perform Time-Tabling and Detectable Precedences in linear time on the Disjunctive constraint. Furthermore, we present a linear-time Overload Checking for the Disjunctive and Cumulative constraints. Finally, we show how the rule of Not-first/Not-last can be enforced in quadratic time for the Cumulative constraint. These algorithms rely on the union find data structure, from which we take advantage to introduce a new data structure that we call it time line. This data structure provides constant time operations that were previously implemented in logarithmic time by the Θ-tree data structure. Experiments show that these new algorithms are competitive even for a small number of tasks and outperform existing algorithms as the number of tasks increases. We also show that the time line can be used to solve specific scheduling problems.

中文翻译：

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用于析取约束的线性时间过滤算法和用于累积非第一非最后的二次过滤算法

我们提出了用于析取和累积约束的新过滤算法，每个过滤算法都将log- n系数提高了最新算法的复杂度。我们展示如何在执行时间和制表可检测优先次序以线性时间析取约束。此外，我们提出了析取和累积约束的线性时间过载检查。最后，我们展示了累积时间如何可以在二次时间内执行非优先/非最后规则约束。这些算法依赖于联合查找数据结构，我们利用该数据结构引入了一种称为时间轴的新数据结构。此数据结构提供了恒定时间操作，该操作先前已由Θ树数据结构以对数时间实现。实验表明，即使对于少量任务，这些新算法也具有竞争力，并且随着任务数量的增加，它们的性能优于现有算法。我们还显示了时间线可用于解决特定的调度问题。