Related papers: Weighted Popular Matchings
In this paper, we give a simple characterization of a set of popular matchings defined by preference lists with ties. By employing our characterization, we propose a polynomial time algorithm for finding a minimum cost popular matching.
The issue of popularity bias -- where popular items are disproportionately recommended, overshadowing less popular but potentially relevant items -- remains a significant challenge in recommender systems. Recent advancements have seen the…
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…
Fairness in machine learning has been studied by many researchers. In particular, fairness in recommender systems has been investigated to ensure the recommendations meet certain criteria with respect to certain sensitive features such as…
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…
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…
Given a set $A$ of $n$ people and a set $B$ of $m \geq n$ items, with each person having a list that ranks his/her preferred items in order of preference, we want to match every person with a unique item. A matching $M$ is called popular if…
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…
To cope with the accelerating pace of technological changes, talents are urged to add and refresh their skills for staying in active and gainful employment. This raises a natural question: what are the right skills to learn? Indeed, it is a…
We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
We are given a bipartite graph $G = \left( A \cup B, E \right)$. In the one-sided model, every $a \in A$ (often called agents) ranks its neighbours $z \in N_{a}$ strictly, and no $b \in B$ has any preference order over its neighbours $y \in…
We study the problem of aggregating individual preferences over alternatives into a collective ranking. A distinctive feature of our setting is that agents are matched to alternatives. Applications include rankings of colleges or academic…
Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is…
The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Van Zuylen et al. [35] introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking of all candidates. A popular ranking $\pi$ of the candidates is at least as good as any other ranking $\sigma$…
Items popularity is a strong signal in recommendation algorithms. It strongly affects collaborative filtering approaches and it has been proven to be a very good baseline in terms of results accuracy. Even though we miss an actual…
When dealing with subjective, noisy, or otherwise nebulous features, the "wisdom of crowds" suggests that one may benefit from multiple judgments of the same feature on the same object. We give theoretically-motivated `feature…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…