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Simpler Approximation for Stable Marriage

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Encyclopedia of Algorithms

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Years and Authors of Summarized Original Work

  • 2013; Király

Introduction

We have a two-sided market, one side is a set U of men, the other side is a set V of women. The first part of the input also contains the mutually acceptable man-woman pairs E. This makes up a bipartite graph \(G(U \cup V\), E). The second part of the input contains the preference lists of each person, that is a weak order (may contain ties) on his/her acceptable pairs.

A matching is a set of mutually disjoint acceptable man-woman pairs. Given a matching M, a man m and a woman w form a blocking pair, if they are an acceptable pair but are not partners in M, and they both prefer each other to their partner, or have no partner in M. That is either w is unmatched in M or w prefers m to her M-partner, and either m is unmatched in M or m prefers w to his M-partner. A matching M is stable if there are no blocking pairs.

We consider a two-sided market under incomplete preference lists with ties (SMTI), where the goal is...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science, Eötvös Loránd University, Budapest, Hungary

    Zoltán Király

  2. Egerváry Research Group (MTA-ELTE), Eötvös Loránd University, Budapest, Hungary

    Zoltán Király

Authors
  1. Zoltán Király
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Corresponding author

Correspondence to Zoltán Király .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Király, Z. (2016). Simpler Approximation for Stable Marriage. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_676

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