Related papers: Random Popular Matchings with Incomplete Preferenc…
For a set $A$ of $n$ people and a set $B$ of $m$ items, with each person having a preference list that ranks all items from most wanted to least wanted, we consider the problem of matching every person with a unique item. A matching $M$ is…
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 an extension of the {\em popular matching} problem in this paper. The input to the popular matching problem is a bipartite graph G = (A U B,E), where A is a set of people, B is a set of items, and each person a belonging to A…
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…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among…
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 $b \in B$…
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…
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 $M'$…
Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable…
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…
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…
We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an…
The popular matching problem is of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in the order of preference, possibly with ties. A matching M is popular if…
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 the cheating strategies for the popular matchings problem. The popular matchings problem can be defined as follows: Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and the edges…
We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list ranking a subset of the jobs. A matching M is popular if there is no other matching M' such that the weight of the applicants…
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…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…
We study the evolution of preferences in multi-population settings that allow matches across distinct populations. Each individual has subjective preferences over potential outcomes, and chooses a best response based on his preferences and…