Popular Matchings with Two-Sided Preferences and One-Sided Ties

Popular Matchings with Two-Sided Preferences and One-Sided Ties

We are given a bipartite graph G = (A ∪ B,E) where each vertex has a preference list ranking its neighbors: in particular, every a ∈ A ranks its neighbors in a strict order of preference, whereas the preference lists of b ∈ B may contain ties. A matching M is popular if there is no matching M ′ such that the number of vertices that prefer M ′ to M exceeds the number that prefer M to M ′. We sho...

One - sided Versus Two - sided Error in

On one-sided versus two-sided classification

One-sided classiiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 ii the set on the input belongs to the given class. Such a classiier is two-sided if the sequence of its output in addition converges to 0 on sets not belonging to the class. The present work obtains the below mentioned results for one-sided classes (...

A One-sided Matching with Dynamic Preferences

In recent years, the problem of allocating indivisible resources to self-interested agents has generated an interesting, rich interplay at the interface of computer science, economics, and game theory. Most theoretical frameworks and empirical studies for resource allocation encompass a wide range of desirable economic properties such as efficiency, truthfulness, and fairness. In addition, a br...

Two-sided popular matchings in bipartite graphs with forbidden/forced elements and weights

Two-sided popular matchings in bipartite graphs are a well-known generalization of stable matchings in the marriage setting, and they are especially relevant when preference lists are incomplete. In this case, the cardinality of a stable matching can be as small as half the size of a maximum matching. Popular matchings allow for assignments of larger size while still guaranteeing a certain fair...