Maximum Locally Stable Matchings

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.