Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial time is best possible. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.

中文翻译：

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周期性定时中的周期不等式分离

周期不平等在公共交通中周期性时间表问题的多面体研究中起着重要作用。我们给出了周期不等式的第一个伪多项式时间分离算法，并且为变化周期不等式的伪多项式时间可分离性提供了严格的证明。此外，我们提供了几个NP完备性结果，表明伪多项式时间是最好的。这些切割平面的效率在周期性时间表问题的实际实例中得到了证明。