article

On a generalization of the stable roommates problem

Authors:

Katarína Cechlárová,

Tamás FleinerAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 1, Issue 1

Pages 143 - 156

https://doi.org/10.1145/1077464.1077474

Published: 01 July 2005 Publication History

Abstract

We consider two generalizations of the stable roommates problem: a) we allow parallel edges in the underlying graph, and b) we study a problem with multiple partners. We reduce both problems to the classical stable roommates problem and describe an extension of Irving's algorithm that solves the generalized problem efficiently. We give a direct proof of a recent result on the structure of stable many-to-many matchings (so called stable b-matchings) as a by-product of the justification of the algorithm.

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Fleiner, T. 2002b. Some results on stable matchings and fixed points. Tech. Rep. TR-2002-8, EGRES ISSN 1587-4451. Available at http://www.cs.elte.hu/egres.

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Cited By

Biró PCsáji G(2024)Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domainsGames and Economic Behavior10.1016/j.geb.2024.03.010145(217-238)Online publication date: May-2024
https://doi.org/10.1016/j.geb.2024.03.010
Danilov V(2023)Review of the Theory of Stable Matchings and Contract SystemsЖурнал вычислительной математики и математической физики10.31857/S004446692303006763:3(491-516)Online publication date: 1-Mar-2023
https://doi.org/10.31857/S0044466923030067
Danilov V(2023)Review of the Theory of Stable Matchings and Contract SystemsComputational Mathematics and Mathematical Physics10.1134/S096554252303006563:3(466-490)Online publication date: 2-May-2023
https://doi.org/10.1134/S0965542523030065
Show More Cited By

Index Terms

On a generalization of the stable roommates problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 1, Issue 1

July 2005

176 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1077464

Issue’s Table of Contents

Copyright © 2005 ACM.

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Publication History

Published: 01 July 2005

Published in TALG Volume 1, Issue 1

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Cited By

Biró PCsáji G(2024)Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domainsGames and Economic Behavior10.1016/j.geb.2024.03.010145(217-238)Online publication date: May-2024
https://doi.org/10.1016/j.geb.2024.03.010
Danilov V(2023)Review of the Theory of Stable Matchings and Contract SystemsЖурнал вычислительной математики и математической физики10.31857/S004446692303006763:3(491-516)Online publication date: 1-Mar-2023
https://doi.org/10.31857/S0044466923030067
Danilov V(2023)Review of the Theory of Stable Matchings and Contract SystemsComputational Mathematics and Mathematical Physics10.1134/S096554252303006563:3(466-490)Online publication date: 2-May-2023
https://doi.org/10.1134/S0965542523030065
Danilov VKarzanov A(2023)Stable and meta-stable contract networksJournal of Mathematical Economics10.1016/j.jmateco.2023.102888108(102888)Online publication date: Oct-2023
https://doi.org/10.1016/j.jmateco.2023.102888
Fenoaltea EBaybusinov INa XZhang Y(2022)A local interaction dynamic for the matching problemPhysica A: Statistical Mechanics and its Applications10.1016/j.physa.2022.127690604(127690)Online publication date: Oct-2022
https://doi.org/10.1016/j.physa.2022.127690
Bredereck RHeeger KKnop DNiedermeier R(2022)Parameterized complexity of stable roommates with ties and incomplete lists through the lens of graph parametersInformation and Computation10.1016/j.ic.2022.104943289(104943)Online publication date: Nov-2022
https://doi.org/10.1016/j.ic.2022.104943
Atef Yekta HBergman DDay R(2022)Balancing stability and efficiency in team formation as a generalized roommate problemNaval Research Logistics (NRL)10.1002/nav.2208470:1(72-88)Online publication date: 8-Dec-2022
https://doi.org/10.1002/nav.22084
Boehmer NBredereck RHeeger KNiedermeier R(2021)Bribery and Control in Stable MarriageJournal of Artificial Intelligence Research10.1613/jair.1.1275571(993-1048)Online publication date: 10-Sep-2021
https://dl.acm.org/doi/10.1613/jair.1.12755
Biró PGudmundsson J(2021)Complexity of finding Pareto-efficient allocations of highest welfareEuropean Journal of Operational Research10.1016/j.ejor.2020.03.018291:2(614-628)Online publication date: Jun-2021
https://doi.org/10.1016/j.ejor.2020.03.018
Nicolò ASen AYadav S(2019)Matching with partners and projectsJournal of Economic Theory10.1016/j.jet.2019.104942184(104942)Online publication date: Nov-2019
https://doi.org/10.1016/j.jet.2019.104942
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