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Algorithmica

pp 1–29 | Cite as

Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case

  • Hugo GilbertEmail author
  • Olivier Spanjaard
Article
  • 6 Downloads

Abstract

This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents’ disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the GGI criterion.

Keywords

Stable marriage problem Fairness Generalized Gini index Complexity 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Gran Sasso Science InstituteL’AquilaItaly
  2. 2.Laboratoire d’Informatique de Paris 6, LIP6, CNRSSorbonne UniversitéParisFrance

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