Multidimensional Stable Roommates with Master List

by   Robert Bredereck, et al.

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.


page 1

page 2

page 3

page 4


Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems

When computing stable matchings, it is usually assumed that the preferen...

Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be alloc...

Stable Marriage with Multi-Modal Preferences

We introduce a generalized version of the famous Stable Marriage problem...

Three-Dimensional Popular Matching with Cyclic Preferences

Two actively researched problem settings in matchings under preferences ...

Pairwise preferences in the stable marriage problem

We study the classical, two-sided stable marriage problem under pairwise...

Modelling the Socialization of Creative Agents in a Master-Apprentice Setting

This paper presents work on modelling the social psychological aspect of...

Stable variation in multidimensional competition

The Fundamental Theorem of Language Change (Yang, 2000) implies the impo...