License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2020.20
URN: urn:nbn:de:0030-drops-120945
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12094/
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Cooper, Frances ; Manlove, David

Algorithms for New Types of Fair Stable Matchings

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LIPIcs-SEA-2020-20.pdf (0.6 MB)


Abstract

We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). For an instance I of SMI there may be many stable matchings, providing significantly different outcomes for the sets of men and women. We introduce two new notions of fairness in SMI. Firstly, a regret-equal stable matching minimises the difference in ranks of a worst-off man and a worst-off woman, among all stable matchings. Secondly, a min-regret sum stable matching minimises the sum of ranks of a worst-off man and a worst-off woman, among all stable matchings. We present two new efficient algorithms to find stable matchings of these types. Firstly, the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d₀ nm) time, where d₀ is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, n is the number of men or women, and m is the total length of all preference lists. Secondly, the Min-Regret Sum Algorithm finds a min-regret sum stable matching in O(d_s m) time, where d_s is the difference in the ranks between a worst-off man in each of the woman-optimal and man-optimal stable matchings. Experiments to compare several types of fair optimal stable matchings were conducted and show that the Regret-Equal Degree Iteration Algorithm produces matchings that are competitive with respect to other fairness objectives. On the other hand, existing types of "fair" stable matchings did not provide as close an approximation to regret-equal stable matchings.

BibTeX - Entry

@InProceedings{cooper_et_al:LIPIcs:2020:12094,
  author =	{Frances Cooper and David Manlove},
  title =	{{Algorithms for New Types of Fair Stable Matchings}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Simone Faro and Domenico Cantone},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12094},
  URN =		{urn:nbn:de:0030-drops-120945},
  doi =		{10.4230/LIPIcs.SEA.2020.20},
  annote =	{Keywords: Stable marriage, Algorithms, Optimality, Fair stable matchings, Regret-equality, Min-regret sum}
}

Keywords: Stable marriage, Algorithms, Optimality, Fair stable matchings, Regret-equality, Min-regret sum
Collection: 18th International Symposium on Experimental Algorithms (SEA 2020)
Issue Date: 2020
Date of publication: 12.06.2020
Supplementary Material: https://zenodo.org/record/3630383 and https://zenodo.org/record/3630349


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