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Three-sided stable matching problem with two of them as cooperative partners

Author

Listed:
  • Liwei Zhong

    (Shanghai University)

  • Yanqin Bai

    (Shanghai University)

Abstract

In this paper, three-sided stable matching problem is discussed, in which two sets, $$V_1$$ V 1 and $$V_2$$ V 2 are cooperative partners, and the agent of the other set U has a strict preference to the agents of set $$V_1$$ V 1 and set $$V_2$$ V 2 respectively. On the other side, the agents of set $$V_1$$ V 1 and set $$V_2$$ V 2 have a strict preference to the agent of set U . About this three-sided matching problem, this paper gives the definition of stable matching, proves that the problem must have a stable matching, and gives an algorithm that can obtain a stable matching.

Suggested Citation

  • Liwei Zhong & Yanqin Bai, 2019. "Three-sided stable matching problem with two of them as cooperative partners," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 286-292, January.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:1:d:10.1007_s10878-017-0224-z
    DOI: 10.1007/s10878-017-0224-z
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    References listed on IDEAS

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    Cited by:

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    2. Feng Zhang & Liwei Zhong, 2021. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 928-936, November.
    3. Jorge Arenas & Juan Pablo Torres-Martínez, 2023. "Reconsidering the existence of stable solutions in three-sided matching problems with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-8, March.
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    6. Jing Fan & Hui Shi, 0. "A three-stage supply chain scheduling problem based on the nursing assistants’ daily work in a hospital," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    7. Jing Fan & Hui Shi, 2021. "A three-stage supply chain scheduling problem based on the nursing assistants’ daily work in a hospital," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 896-908, November.
    8. Qian Li & Wei Zhang, 2021. "An improved linear convergence of FISTA for the LASSO problem with application to CT image reconstruction," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 831-847, November.
    9. Xuerui Gao & Yanqin Bai & Qian Li, 0. "A sparse optimization problem with hybrid $$L_2{\text {-}}L_p$$L2-Lp regularization for application of magnetic resonance brain images," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-25.
    10. He Huang & Wei Gao & Chunming Ye, 0. "An intelligent data-driven model for disease diagnosis based on machine learning theory," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.
    11. He Huang & Wei Gao & Chunming Ye, 2021. "An intelligent data-driven model for disease diagnosis based on machine learning theory," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 884-895, November.

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