Related papers: Popularity at Minimum Cost
Let $G$ be a bipartite graph where every node has a strict ranking of its neighbors. For every node, its preferences over neighbors extend naturally to preferences over matchings. Matching $N$ is more popular than matching $M$ if the number…
In the Popular Matching problem, we are given a bipartite graph $G = (A \cup B, E)$ and for each vertex $v\in A\cup B$, strict preferences over the neighbors of $v$. Given two matchings $M$ and $M'$, matching $M$ is more popular than $M'$…
We consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…
We are given a bipartite graph $G = (A \cup B, E)$ where each vertex has a preference list ranking its neighbors: in particular, every $a \in A$ ranks its neighbors in a strict order of preference, whereas the preference lists of $b \in B$…
Let $G = (A \cup B,E)$ be a bipartite graph where the set $A$ consists of agents or main players and the set $B$ consists of jobs or secondary players. Every vertex has a strict ranking of its neighbors. A matching $M$ is popular if for any…
We consider the max-size popular matching problem in a roommates instance G = (V,E) with strict preference lists. A matching M is popular if there is no matching M' in G such that the vertices that prefer M' to M outnumber those that prefer…
Let G = ((A,B),E) be an instance of the stable marriage problem where every vertex ranks its neighbors in a strict order of preference. A matching M in G is popular if M does not lose a head-to-head election against any matching. Popular…
Our input is a complete graph $G = (V,E)$ on $n$ vertices where each vertex has a strict ranking of all other vertices in $G$. Our goal is to construct a matching in $G$ that is popular. A matching $M$ is popular if $M$ does not lose a…
Popularity is an approach in mechanism design to find fair structures in a graph, based on the votes of the nodes. Popular matchings are the relaxation of stable matchings: given a graph G=(V,E) with strict preferences on the neighbors of…
An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there…
In the popular edge problem, the input is a bipartite graph $G = (A \cup B,E)$ where $A$ and $B$ denote a set of men and a set of women respectively, and each vertex in $A\cup B$ has a strict preference ordering over its neighbours. A…
We consider popular matching problems in both bipartite and non-bipartite graphs with strict preference lists. It is known that every stable matching is a min-size popular matching. A subclass of max-size popular matchings called dominant…
We consider a matching problem in a bipartite graph $G=(A\cup B,E)$ where nodes in $A$ are agents having preferences in partial order over their neighbors, while nodes in $B$ are objects without preferences. We propose a polynomial-time…
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…
Given a bipartite graph G = (A u B, E) with strict preference lists and and edge e*, we ask if there exists a popular matching in G that contains the edge e*. We call this the popular edge problem. A matching M is popular if there is no…
For a set A of n applicants and a set I of m items, we consider a problem of computing a matching of applicants to items, i.e., a function M mapping A to I; here we assume that each applicant $x \in A$ provides a preference list on items in…
We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…
In a graph where vertices have preferences over their neighbors, a matching is called popular if it does not lose a head-to-head election against any other matching when the vertices vote between the matchings. Popular matchings can be seen…
Our input is a bipartite graph $G = (A \cup B,E)$ where each vertex in $A \cup B$ has a preference list strictly ranking its neighbors. The vertices in $A$ and in $B$ are called students and courses, respectively. Each student $a$ seeks to…
We consider the many-to-many bipartite matching problem in the presence of two-sided preferences and two-sided lower quotas. The input to our problem is a bipartite graph G=(A U B, E), where each vertex in A U B specifies a strict…