(n2) algorithm (where n = |A B|) for the popular matching problem in this model. Note that this model is quite different … matching M is popular if there is no matching M' such that the number of vertices that prefer M' to M exceeds the number of … vertices that prefer M to M'. We show that the problem of deciding whether G admits a popular matching or not is NP-hard. This …

We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected … maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching … edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and …

-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show … that this problem is NP-hard even if d = 3. On the positive side we give a 2d+3 / 7-approximation algorithm for d {3, 4, 5 …-SRTI admits a stable matching is NP-complete even if d = 3. We also consider the "most stable" version of this problem and prove a …

order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election … against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of … popular matchings that always exist and can be easily computed is the set of dominant matchings. A popular matching M is …

goal is to construct a matching in G that is "globallystable" or popular. A matching M is popular if M does not lose a head …-to-head election againstany matching M': here each vertex casts a vote forthe matching in {M,M'} in which it gets abetter assignment … not. The popular matching problem in Gis easy to solve for odd n. Surprisingly, the problem becomes NP-hard for even n, as …

matching algorithm – originally designed by Gale and Shapley (1962) for the college admissions problem – was imbued with … than directly applying the theory of simple markets; (Roth, 2010). The deferred acceptance matching algorithm and its … understand their accomplishments, reviews successful matching processes adopted in particular market institutions. In some …

. We devise a machine learning-based matching system that identifies users with high expected value and provides them the … mechanisms that drive the impact of the matching system …

matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an efficient algorithm for … computing one of them. The outcome of the algorithm belongs to an absorbing set. …