A many-to-many ‘rural hospital theorem’

Klijn, Flip; Yazıcı, Ayşe Canan

doi:10.1016/j.jmateco.2014.09.003

Cited by 18 publications

(5 citation statements)

References 32 publications

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“…Pairwise stability means the lack of a single blocking contract. Roth showed that setwise and pairwise stable solutions coincide and exist for specific substitutable choice functions, and a number of extensions and structural results have been obtained in the follow-up literature [19], [4], [8], [13], [14].…”

Section: Introductionmentioning

confidence: 95%

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Strong core and Pareto-optimal solutions for the multiple partners matching problem under lexicographic preferences

Bíró¹,

Csáji²

2022

Preprint

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In a multiple partners matching problem the agents can have multiple partners up to their capacities. In this paper we consider both the twosided many-to-many stable matching problem and the one-sided stable fixtures problem under lexicographic preferences. We study strong core and Pareto-optimal solutions for this setting from a computational point of view. First we provide an example to show that the strong core can be empty even under these severe restrictions for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. We also show that for a given matching checking Pareto-optimality and the strong core properties are co-NP-complete problems for the many-to-many problem, and deciding the existence of a complete Pareto-optimal matching is also NP-hard for the fixtures problem. On the positive side, we give efficient algorithms for finding a near feasible strong core solution, where the capacities are only violated by at most one unit for each agent, and also for finding a half-matching in the strong core of fractional matchings. These polynomial time algorithms are based on the Top Trading Cycle algorithm. Finally, we also show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems, which is in contrast with the hardness result for the fixtures problem.

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Section: Introductionmentioning

confidence: 95%

“…Klaus and Walzl studied special versions of setwise stability under different domain restrictions on substitutable preferences [13]. Klijn and Yazici proved that the rural hospitals theorem holds for substitutable and weakly separable preferences in many-to-many markets [14].…”

Section: Related Literaturementioning

confidence: 99%

Strong core and Pareto-optimal solutions for the multiple partners matching problem under lexicographic preferences

Bíró¹,

Csáji²

2022

Preprint

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“…Chaque organisation possède des membres faisant aussi partie d'autres organisations. Le problème se rapproche alors d'un problème de formation de coalitions avec chevauchement des coalitions [18].…”

Section: Choix Social Informatiqueunclassified

ABSG : une architecture d’agents d’inspiration sociale pour le problème de formation de coalitions

Bettinelli¹,

Occello²,

Genthial³

2023

Revue Ouverte d'Intelligence Artificielle

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“…Many-to-many extensions of sm (and by implication hr) have been considered in the literature (Roth, 1984b;Roth and Sotomayor, 1990;Sotomayor, 1999;Baïou and Balinski, 2000;Fleiner, 2003;Martínez et al, 2004;Echenique and Oviedo, 2006;Bansal et al, 2007;Kojima andÜnver, 2008;Eirinakis et al, 2012Eirinakis et al, , 2013Klijn and Yazıcı, 2014). These matching problems tend to be described in the context of assigning workers to firms, where each agent can be multiply assigned (up to a given capacity).…”

Section: Many-to-many Stable Matchingmentioning

confidence: 99%