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Stable Marriage with Ties and Incomplete Lists

2007; Iwama, Miyazaki, Yamauchi

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Encyclopedia of Algorithms

Keywords and Synonyms

Stable matching problem          

Problem Definition

In the original setting of the stable marriage problem introduced by Gale and Shapley [2], each preference list has to include all members of the other party, and furthermore, each preference list must be totally ordered (see entry Stable Marriage also).

One natural extension of the problem is then to allow persons to include ties in preference lists. In this extension, there are three variants of the stability definition, super-stability, strong stability, and weak stability (see below for definitions). In the first two stability definitions, there are instances that admit no stable matching, but there is a polynomial-time algorithm in each case that determines if a given instance admits a stable matching, and finds one if exists [8]. On the other hand, in the case of weak stability, there always exists a stable matching and one can be found in polynomial time.

Another possible extension is to allow persons to declare...

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Recommended Reading

  1. Canadian Resident Matching Service (CaRMS) http://www.carms.ca/. Accessed 27 Feb 2008, JST

  2. Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Monthly 69, 9–15 (1962)

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  4. Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Boston, MA (1989)

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  5. Halldórsson, M.M., Irving, R.W., Iwama, K., Manlove, D.F., Miyazaki, S., Morita, Y., Scott, S.: Approximability results for stable marriage problems with ties. Theor. Comput. Sci. 306, 431–447 (2003)

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  15. Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: Strongly stable matchings in time O(nm) and extension to the hospitals-residents problem. Proc. STACS 2004. LNCS (2996), pp. 222–233. (2004)

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Author information

Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto, Japan

    Kazuo Iwama

  2. Academic Center for Computing and Media Studies, Kyoto University, Kyoto, Japan

    Shuichi Miyazaki

Authors
  1. Kazuo Iwama
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  2. Shuichi Miyazaki
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Iwama, K., Miyazaki, S. (2008). Stable Marriage with Ties and Incomplete Lists. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_395

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