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Pairwise Preferences in the Stable Marriage Problem

Authors Ágnes Cseh , Attila Juhos

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Author Details

Ágnes Cseh
  • Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, 1097 Budapest, Tóth Kálmán u. 4., Hungary
Attila Juhos
  • Department of Computer Science and Information Theory, Budapest University of Technology and Economics, 1117 Budapest, Magyar Tudósok krt. 2., Hungary

Funding

This work was supported by the Cooperation of Excellences Grant (KEP-6/2018), by the Ministry of Human Resources under its New National Excellence Programme (ÚNKP-18-4-BME-331 and ÚNKP-18-1-I-BME-309), the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2016), its János Bolyai Research Fellowship, and OTKA grant K128611.

Acknowledgements

The authors thank Tamás Fleiner, David Manlove, and Dávid Szeszlér for fruitful discussions on the topic.

Cite AsGet BibTex

Ágnes Cseh and Attila Juhos. Pairwise Preferences in the Stable Marriage Problem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.STACS.2019.21

Abstract

We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to declare a draw or even withdraw from such a comparison. This freedom is then gradually restricted as we specify six stages of orderedness in the preferences, ending with the classical case of strictly ordered lists. We study all cases occurring when combining the three known notions of stability - weak, strong and super-stability - under the assumption that each side of the bipartite market obtains one of the six degrees of orderedness. By designing three polynomial algorithms and two NP-completeness proofs we determine the complexity of all cases not yet known, and thus give an exact boundary in terms of preference structure between tractable and intractable cases.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • stable marriage
  • intransitivity
  • acyclic preferences
  • poset
  • weakly stable matching
  • strongly stable matching
  • super stable matching

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