This paper constitutes a step forward in resource-constrained scheduling theory. We introduce an $O(n\times \alpha (n)\times \log n)$ checker for energetic reasoning (ER), where $\alpha \left(n\right)$ is Ackermann's inverse function. Until now, after more than 20 years of research, the best technique, recently obtained by Ouellet and Quimper, was in $O(n{\log }^{2}n)$. We identify mathematical properties that allow the number of useful intervals to be reduced. We also discuss the interest of integrating this checker into industrial solvers developed for addressing optimisation problems.

中文翻译：

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累积调度问题的能量推理的更快检查器

本文构成了资源受限调度理论的一个进步。我们介绍一个$○(n\times \alpha (n)\times \mathrm{日志}n)$能量推理检查器 (ER)，其中$\alpha \left(n\right)$是阿克曼的反函数。直到现在，经过 20 多年的研究，最近由 Ouellet 和 Quimper 获得的最佳技术在$○(n{\mathrm{日志}}^{2}n)$. 我们确定了允许减少有用间隔数量的数学属性。我们还讨论了将此检查器集成到为解决优化问题而开发的工业求解器中的兴趣。