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URN: urn:nbn:de:0030-drops-95238
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Finding Stable Matchings That Are Robust to Errors in the Input

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Abstract

In this paper, we introduce the issue of finding solutions to the stable matching problem that are robust to errors in the input and we obtain the first algorithmic results on this topic. In the process, we also initiate work on a new structural question concerning the stable matching problem, namely finding relationships between the lattices of solutions of two "nearby" instances. Our main algorithmic result is the following: We identify a polynomially large class of errors, D, that can be introduced in a stable matching instance. Given an instance A of stable matching, let B be the instance that results after introducing one error from D, chosen via a discrete probability distribution. The problem is to find a stable matching for A that maximizes the probability of being stable for B as well. Via new structural properties of the type described in the question stated above, we give a polynomial time algorithm for this problem.

BibTeX - Entry

@InProceedings{mai_et_al:LIPIcs:2018:9523,
  author =	{Tung Mai and Vijay V. Vazirani},
  title =	{{Finding Stable Matchings That Are Robust to Errors in the Input}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{60:1--60:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9523},
  URN =		{urn:nbn:de:0030-drops-95238},
  doi =		{10.4230/LIPIcs.ESA.2018.60},
  annote =	{Keywords: Stable Matching, Robust}
}

Keywords: Stable Matching, Robust
Seminar: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue date: 2018
Date of publication: 2018


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