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European Symposium on Algorithms

ESA 2004: Algorithms – ESA 2004 pp 508–519Cite as

On the Stability of Multiple Partner Stable Marriages with Ties

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

Abstract

We consider the generalized version of the stable marriage problem where each man and woman’s preference list may have ties. Furthermore, each man and woman wishes to be matched to as many of acceptable partners as possible, up to his or her specified quota. Many-to-many version of the stable marriage problem has wide applications in matching retailers and shopkeepers in e-marketplaces. We investigate different forms of stability in this context and describe an algorithm to find strongly stable matchings (if one exists) in the context of multiple partner stable marriage problem with ties. In the context of Hospital-Residents problem for which only the resident-oriented algorithm for finding a strongly stable matching is known, this algorithm gives a hospital-oriented version (for the same) as well. Furthermore, in any instance of many-to-many stable marriage problem with ties, we show that the set of strongly stable matchings forms a distributive lattice. The results in this paper extend those already known for the one-to-one version and many-to-one version (Hospitals-Residents problem) of the problem.

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, 94305, USA

    Varun S. Malhotra

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  1. Varun S. Malhotra
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Editor information

Editors and Affiliations

  1. University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer Science, King’s College, WC2R 2LS, London, UK

    Tomasz Radzik

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© 2004 Springer-Verlag Berlin Heidelberg

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Malhotra, V.S. (2004). On the Stability of Multiple Partner Stable Marriages with Ties. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_46

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  • DOI: https://doi.org/10.1007/978-3-540-30140-0_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

  • eBook Packages: Springer Book Archive

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