Related papers: Extending Stable and Popular Matching Algorithms f…
The stable matching problem is one of the central problems of algorithmic game theory. If participants are allowed to have ties, the problem of finding a stable matching of maximum cardinality is an NP-hard problem, even when the ties are…
We give a sharp lower bound on the number of matchings of a given size in a bipartite graph. When specialized to regular bipartite graphs, our results imply Friedland's Lower Matching Conjecture and Schrijver's theorem proven by Gurvits and…
Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
We study the Second Price Matching problem, introduced by Azar, Birnbaum, Karlin, and Nguyen in 2009. In this problem, a bipartite graph (bidders and goods) is given, and the profit of a matching is the number of matches containing a second…
The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a…
We introduce a new and broader formulation of the stable marriage problem (SMP), called the stable polygamy problem (SPP), where multiple individuals from a larger group $L$ of $|L|$ individuals can be matched with a single individual from…
The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely…
Given a set $A$ of $n$ people, with each person having a preference list that ranks a subset of $A$ as his/her acceptable partners in order of preference, we consider the Roommates Problem (RP) and the Marriage Problem (MP) of matching…
Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two "nearby" instances of stable matching. They also gave an application of their work to finding…
We study a practical centralized matching problem which assigns children to daycare centers. The collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as…
In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of \emph{arbitrary}…
Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous…
Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to…
We study ordinal approximation algorithms for maximum-weight bipartite matchings. Such algorithms only know the ordinal preferences of the agents/nodes in the graph for their preferred matches, but must compete with fully omniscient…
As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for computing $\ell$ disjoint stable matchings with minimum total…
The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…
In this paper, we generalize the recently studied Stochastic Matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the Stochastic Matching problem that has…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the…