  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.
