Finding Stable Matchings That Are Robust to Errors in the Input

Authors Tung Mai, Vijay V. Vazirani

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Author Details

Tung Mai
  • Georgia Institute of Technology, Atlanta, GA, USA
Vijay V. Vazirani
  • University of California, Irvine, Irvine, CA, USA

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Tung Mai and Vijay V. Vazirani. Finding Stable Matchings That Are Robust to Errors in the Input. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 60:1-60:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Stable Matching
  • Robust


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