Since the early days of research in algorithms and complexity, the computation of stable matchings is a core topic. While in the classic setting the goal is to match up two agents (either from different "gender" (this is Stable Marriage) or "unrestricted" (this is Stable Roommates)), Knuth [1976] triggered the study of three- or multidimensional cases. Here, we focus on the study of Multidimensional Stable Roommates, known to be NP-hard since the early 1990's. Many NP-hardness results, however, rely on very general input instances that do not occur in at least some of the specific application scenarios. With the quest for identifying islands of tractability, we look at the case of master lists. Here, as natural in applications where agents express their preferences based on "objective" scores, one roughly speaking assumes that all agent preferences are "derived from" a central master list, implying that the individual agent preferences shall be similar. Master lists have been frequently studied in the two-dimensional (classic) stable matching case, but seemingly almost never for the multidimensional case. This work, also relying on methods from parameterized algorithm design and complexity analysis, performs a first systematic study of Multidimensional Stable Roommates under the assumption of master lists.

中文翻译：

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多维稳定室友主单

从算法和复杂性研究的早期开始，稳定匹配的计算是一个核心主题。虽然在经典设置中的目标是匹配两个代理（来自不同的“性别”（这是稳定的婚姻）或“不受限制的”（这是稳定的室友）），但 Knuth [1976] 引发了对三维或多维的研究案件。在这里，我们专注于多维稳定室友的研究，自 1990 年代初期以来，它就被认为是 NP-hard。然而，许多 NP-hardness 结果依赖于至少在某些特定应用场景中不会出现的非常一般的输入实例。为了识别易处理岛，我们来看一下主列表的案例。在这里，在代理根据“客观”分数表达偏好的应用程序中，这很自然，粗略地说，假设所有代理偏好都“来自”中央主列表，这意味着个体代理偏好应该是相似的。在二维（经典）稳定匹配情况下经常研究主列表，但似乎几乎从未在多维情况下研究过。这项工作也依赖于参数化算法设计和复杂性分析的方法，在主列表假设下对多维稳定室友进行了首次系统研究。