多维度稳定室友与主列表
Multidimensional Stable Roommates with Master List
摘要：
自算法和复杂性研究的早期以来，稳定匹配的计算一直是一个核心课题。在经典的设定中，目标是匹配两个代理人（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）），Knuth [1976]引发了对三维或多维案例的研究。在这里，我们专注于多维稳定室友的研究，已知自20世纪90年代初以来是NP难的。然而，许多NP难的结果依赖于非常一般的输入实例，这些实例至少在某些特定的应用场景中不会发生。随着寻求确定岛屿的温顺的多维稳定室友，我们研究的情况下，主列表。在这里，作为自然的应用程序中，代理人表达他们的喜好基于“客观”的分数，一个粗略地说，假设所有代理人的喜好是“来自”一个中央主列表，这意味着个人代理人的喜好应该是相似的。主列表经常被研究在二维（经典）稳定匹配的情况下，但似乎几乎从来没有多维的情况下。本工作，也依赖于从参数化算法设计和复杂性分析的方法，进行了第一次系统的研究下，主列表的假设下的多维稳定室友。
英文摘要：
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 for Multidimensional Stable Roommates, we study 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.
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