Pairwise Preferences in the Stable Marriage Problem
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.
stable marriage
intransitivity
acyclic preferences
poset
weakly stable matching
strongly stable matching
super stable matching
Theory of computation~Graph algorithms analysis
21:1-21:16
Regular Paper
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.
All missing proofs can be found in the full version of the paper [Cseh and Juhos, 2018], https://arxiv.org/abs/1810.00392.
The authors thank Tamás Fleiner, David Manlove, and Dávid Szeszlér for fruitful discussions on the topic.
Ágnes
Cseh
Ágnes Cseh
Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, 1097 Budapest, Tóth Kálmán u. 4., Hungary
https://orcid.org/0000-0003-4991-2599
Attila
Juhos
Attila Juhos
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, 1117 Budapest, Magyar Tudósok krt. 2., Hungary
10.4230/LIPIcs.STACS.2019.21
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Ágnes Cseh and Attila Juhos
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