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Improving Man-Optimal Stable Matchings by Minimum Change of Preference Lists
Algorithms 2013, 6(3), 383-395; doi:10.3390/a6030383

Maximum Locally Stable Matchings

1,*  and 2
Received: 4 January 2013; in revised form: 2 June 2013 / Accepted: 4 June 2013 / Published: 24 June 2013
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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Abstract: Motivated by the observation that most companies are more likely to consider job applicants referred by their employees than those who applied on their own, Arcaute and Vassilvitskii modeled a job market that integrates social networks into stable matchings in an interesting way. We call their model HR+SN because an instance of their model is an ordered pair (I, G) where I is a typical instance of the Hospital/Residents problem (HR) and G is a graph that describes the social network (SN) of the residents in I. A matching p, of hospitals and residents has a local blocking pair (h, r) if (h, r) is a blocking pair of ii, and there is a resident r' such that r' is simultaneously an employee of h in the matching and a neighbor of r in G. Such a pair is likely to compromise the matching because the participants have access to each other through r': r can give her resume to r' who can then forward it to h. A locally stable matching is a matching with no local blocking pairs. The cardinality of the locally stable matchings of I can vary. This paper presents a variety of results on computing a locally stable matching with maximum cardinality.
Keywords: stable matchings; hospital/residents problem; social networks stable matchings; hospital/residents problem; social networks
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Cheng, C.T.; McDermid, E. Maximum Locally Stable Matchings. Algorithms 2013, 6, 383-395.

AMA Style

Cheng CT, McDermid E. Maximum Locally Stable Matchings. Algorithms. 2013; 6(3):383-395.

Chicago/Turabian Style

Cheng, Christine T.; McDermid, Eric. 2013. "Maximum Locally Stable Matchings." Algorithms 6, no. 3: 383-395.

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