Random matching under priorities: stability and no envy concepts

Aziz, Haris; Klaus, Bettina

doi:10.1007/s00355-019-01181-x

Cited by 17 publications

(22 citation statements)

References 34 publications

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“…For future works, following Aziz and Klaus [2017], it could be worth investigating the randomized version of the GGI stable marriage problem. By randomized, we mean that we consider mixed stable marriages, and not only deterministic stable marriages.…”

Section: Resultsmentioning

confidence: 99%

Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case

Gilbert

Spanjaard

2019

Algorithmica

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This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents' disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the GGI criterion.: 10 ≻ m 9 4 ≻ m 9 6 ≻ m 9 7 ≻ m 9 9 ≻ m 9 5 ≻ m 9 1 ≻ m 9 2 ≻ m 9 3 ≻ m 9 8 m 10 : 9 ≻ m 10 4 ≻ m 10 5 ≻ m 10 7 ≻ m 10 8 ≻ m 10 6 ≻ m 10

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Section: Resultsmentioning

confidence: 99%

Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case

Gilbert

Spanjaard

2019

Algorithmica

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“…Our definition of fractional stability (in the presence of cardinal preferences) has appeared before in the economics literature [5,10,11,25]. However, these papers focus primarily on the relationship among various notions of stability and economic efficiency, and do not consider computational questions.…”

Section: Further Related Workmentioning

confidence: 99%

Stable fractional matchings

Caragiannis

Filos-Ratsikas

Kanellopoulos

et al. 2021

Artificial Intelligence

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We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable fractional matchings can have much higher social welfare than stable integral ones, our goal is to understand the computational complexity of finding an optimal (i.e., welfare-maximizing) or nearlyoptimal stable fractional matching. We present simple approximation algorithms for this problem with weak welfare guarantees and, rather unexpectedly, we furthermore show that achieving better approximations is hard. This computational hardness persists even for approximate stability. To the best of our knowledge, these are the first computational complexity results for stable fractional matchings. En route to these results, we provide a number of structural observations.

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“…This implies that a Pareto optimal outcome can be found in polynomial time. Researchers have also considered various notions of fairness in the context of the roommate problem [Abdulkadiroglu and Sönmez, 2003;Aziz and Klaus, 2019]. One such notion is envy-freeness: an outcome is said to be envy-free if no agent wants to take the place of another agent.…”

Section: Related Workmentioning

confidence: 99%

Stable Roommate Problem with Diversity Preferences

Boehmer

Elkind

2020

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence

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In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences (Bredereck, Elkind, Igarashi, AAMAS'19): each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents’ preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem.

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Random matching under priorities: stability and no envy concepts

Cited by 17 publications

References 34 publications

Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case

Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case

Stable fractional matchings

Stable Roommate Problem with Diversity Preferences

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