Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.
翻译：在偏好下匹配的两个积极研究的问题设置是大众匹配和三维稳定匹配与周期偏好的问题。 在本文中,我们将第一个专题的最佳概念应用于第二个专题的投入特征。 我们调查了稳定性、受欢迎程度及其严格的变体、强大的稳定性和在三维周期偏好情况下的强烈受欢迎程度之间的联系。 此外,我们还得出了从主列表中得出偏好时这些问题的复杂性的结果。
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