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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ESA.2018.60

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.

Subject Classification

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

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References

  1. A. Ben-Tal, L. El Ghaoui, and A.S. Nemirovski. Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press, October 2009. Google Scholar
  2. G. C. Calafiore and L. El Ghaoui. On distributionally robust chance-constrained linear programs. Journal of Optimization Theory and Applications, 130(1), 2006. Google Scholar
  3. David Gale and Lloyd S Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9-15, 1962. Google Scholar
  4. Begum Genc, Mohamed Siala, Barry O'Sullivan, and Gilles Simonin. Finding robust solutions to stable marriage. arXiv preprint arXiv:1705.09218, 2017. Google Scholar
  5. Begum Genc, Mohamed Siala, Gilles Simonin, and Barry O’Sullivan. On the complexity of robust stable marriage. In International Conference on Combinatorial Optimization and Applications, pages 441-448. Springer, 2017. Google Scholar
  6. Dan Gusfield and Robert W Irving. The stable marriage problem: structure and algorithms. MIT press, 1989. Google Scholar
  7. Robert W Irving. An efficient algorithm for the “stable roommates” problem. Journal of Algorithms, 6(4):577-595, 1985. Google Scholar
  8. Robert W Irving and Paul Leather. The complexity of counting stable marriages. SIAM Journal on Computing, 15(3):655-667, 1986. Google Scholar
  9. Donald Ervin Knuth. Stable marriage and its relation to other combinatorial problems: An introduction to the mathematical analysis of algorithms. American Mathematical Soc., 1997. Google Scholar
  10. Tung Mai and Vijay V. Vazirani. A generalization of Birkhoff’s theorem for distributive lattices, with applications to robust stable matchings. In arXiv, 2018. Google Scholar
  11. David Manlove. Algorithmics of Matching Under Preferences. World Scientific, 2013. Google Scholar
  12. Alvin E. Roth. Al Roth’s game theory, experimental economics, and market design page, 2016. URL: http://stanford.edu/~alroth/alroth.html#MarketDesign.
  13. Alvin E. Roth and Lloyd S. Shapley. The 2012 Nobel Prize in Economics, 2012. URL: https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/.
  14. Wikipedia. Fault Tolerence. URL: https://en.wikipedia.org/wiki/Fault_tolerance.
  15. Wikipedia. Robustness (Computer Science). URL: https://en.wikipedia.org/wiki/Robustness_(computer_science).
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