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Pairwise Preferences in the Stable Marriage Problem

Authors: Ágnes Cseh; Attila Juhos;

Pairwise Preferences in the Stable Marriage Problem

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.

Countries
Hungary, Germany
Keywords

ddc:004, FOS: Computer and information sciences, 330, Discrete Mathematics (cs.DM), acyclic preferences, Hasso-Plattner-Institut für Digital Engineering GmbH, HQ The family. Marriage. Woman / család, 05C70, 68W40, 05C85, super stable matching, poset, C78, stable marriage, ddc:330, strongly stable matching, házasság, 004, weakly stable matching, nőpolitika, C63, intransitivity, Computer Science - Discrete Mathematics, ddc: ddc:004

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Top 10%
Top 10%
Green
bronze