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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
Article

Maximum Locally Stable Matchings

1,*  and 2
1 Department of Computer Science, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53211, USA 2 21CT, 6011 West Courtyard Drive, Austin, TX 78730, USA
* Author to whom correspondence should be addressed.
Received: 4 January 2013 / Revised: 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 (CC BY 3.0).
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Cheng, C.T.; McDermid, E. Maximum Locally Stable Matchings. Algorithms 2013, 6, 383-395.

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