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International Workshop on Algorithms and Computation

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Approximability of Stable Matching Problems

Approximability of Stable Matching Problems

  • Kazuo Iwama18 
  • Conference paper
  • 650 Accesses

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7157)

Abstract

The stable matching problem, also called the stable marriage problem, was first introduced by Gale and Shapley in 1962: In this problem, we are given two parties of men and women, and for each person in one party his/her preference list that orders the members of the other party. The question is to find a stable matching, i.e., a matching containing no pair (blocking pair) of man and woman who prefer each other to their current partners. The above paper gave a linear time algorithm, now called the Gale-Shapley algorithm, for this problem.

The problem has a wide range of real-world applications including assigning residents to hospitals, known as the hospital/residents problem, used in NRMP in US and in many other similar programs. For such large scale applications, however, the original setting that each preference list must be strict and complete is clearly unrealistic. Hence, the study of two natural relaxations, allowing ties and incomplete lists, has been started shortly after the Gale-Shapley paper, and before long it turned out that there are still linear time algorithms, namely the problem does not become inherently harder, if we allow either one of the two relaxations.

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Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Kazuo Iwama

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  1. Kazuo Iwama
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Editors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Bangladesh

    Md. Saidur Rahman

  2. , Faculty of Engineering, Department of Computer Science, Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

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© 2012 Springer-Verlag Berlin Heidelberg

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Iwama, K. (2012). Approximability of Stable Matching Problems. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-28076-4_2

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  • Print ISBN: 978-3-642-28075-7

  • Online ISBN: 978-3-642-28076-4

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