Multidimensional Stable Roommates with Master List

Bredereck, Robert; Heeger, Klaus; Knop, Dušan; Niedermeier, Rolf

doi:10.1007/978-3-030-64946-3_5

Cited by 19 publications

(13 citation statements)

References 27 publications

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“…To be consistent with previous research relating to three-dimensional variants of SR [19,21], in this paper we refer to a partition into triples as a matching rather than a partition and write stable matching rather than core stable partition. We finally remark that the usage of the terminology "three-dimensional" to refer to the coalition size rather than, say, the number of agent sets [24], is consistent with previous work in the literature [1,10,21,26].…”

Section: Introductionsupporting

confidence: 80%

“…In 2020, Bredereck et al considered another variation of multidimensional roommate games involving either a master list or master poset, a central list or poset from which all agents' preference lists are derived [10]. They presented two positive results relating to restrictions of the problem involving a master poset although they showed for either a master list or master poset that finding a stable matching in general remains NP-hard or W[1]-hard, for three very natural parameters.…”

Section: Introductionmentioning

confidence: 99%

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The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

McKay

Manlove

2021

Lecture Notes in Computer Science

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The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A number of three-dimensional variants exist, in which agents are instead matched into triples. Both the original problem and these variants can also be viewed as hedonic games. We formalise a three-dimensional variant using general additively separable preferences, in which each agent provides an integer valuation of every other agent. In this variant, we show that a stable matching may not exist and that the related decision problem is NP-complete, even when the valuations are binary. In contrast, we show that if the valuations are binary and symmetric then a stable matching must exist and can be found in polynomial time. We also consider the related problem of finding a stable matching with maximum utilitarian welfare when valuations are binary and symmetric. We show that this optimisation problem is NPhard and present a novel 2-approximation algorithm.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

McKay

Manlove

2021

Lecture Notes in Computer Science

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“…This type of preference structure is also called a master list. Besides them, Bredereck et al [10] also investigated master lists in the context of 3D stable matchings, and there is a large set of results on 2D stable or popular matchings with master lists in the input [23,24,26,33].…”

Section: Stability In 3 Dimensionsmentioning

confidence: 99%

Three-Dimensional Popular Matching with Cyclic Preferences

Cseh¹,

Peters²

2021

Preprint

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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.

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“…Arkin et al [1] showed that not every instance of Euclid-3DSR admits a 3D stable matching, but left open whether the computational complexity of determining the existence of 3D stable matchings is NP-hard [1]. 1 The same question has been repeatedly asked since then [10,13,6,18,5].…”

Section: Introductionmentioning

confidence: 99%

“…Other generalized variants include the study of 3D stable matchings with cyclic preferences [7,3,12], with preferences over individuals [10], and the study of the higher-dimensional case [5] and of other restricted preference domains [4].…”

Section: Introductionmentioning

confidence: 99%

Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

Roy¹

2021

Preprint

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We establish NP-completeness for the Euclidean 3-Dimensional Stable Roommates problem, which asks whether a given set V of 3n points from the Euclidean space can be partitioned into n disjoint (unordered) triples Π = {V 1 , . . . , V n } such that Π is stable. Here, stability means that no three points x, y, z ∈ V are blocking Π, and x, y, z ∈ V are said to be blocking Π if the following is satisfied:-δ(x, y) + δ(x, z) < δ(x, x 1 ) + δ(x, x 2 ), -δ(y, x) + δ(y, z) < δ(y, y 1 ) + δ(y, y 2 ), and -δ(z, x) + δ(z, y) < δ(z, z 1 ) + δ(z, z 2 ), where {x, x 1 , x 2 }, {y, y 1 , y 2 }, {z, z 1 , z 2 } ∈ Π, and δ(a, b) denotes the Euclidean distance between a and b.

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Multidimensional Stable Roommates with Master List

Cited by 19 publications

References 27 publications

The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

Three-Dimensional Popular Matching with Cyclic Preferences

Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

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