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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…

Data Structures and Algorithms · Computer Science 2018-04-10 Telikepalli Kavitha

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a…

Computer Science and Game Theory · Computer Science 2015-03-17 Itai Ashlagi , Mark Braverman , Avinatan Hassidim

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…

Data Structures and Algorithms · Computer Science 2019-12-23 Changyong Hu , Vijay K. Garg

The stable marriage problem with ties is a well-studied and interesting problem in game theory. We are given a set of men and a set of women. Each individual has a preference ordering on the opposite group, which can possibly contain ties.…

Discrete Mathematics · Computer Science 2020-03-24 Felix Bauckholt , Laura Sanità

We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…

Data Structures and Algorithms · Computer Science 2018-04-04 Tung Mai , Vijay V. Vazirani

This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…

Theoretical Economics · Economics 2023-09-11 Chao Huang

We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the…

Computer Science and Game Theory · Computer Science 2021-08-11 James P. Bailey , Craig A. Tovey

In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in $O(n^2)$ communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each…

Computer Science and Game Theory · Computer Science 2015-04-03 Rafail Ostrovsky , Will Rosenbaum

We present a polynomial-time $\frac{3}{2}$-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem…

Data Structures and Algorithms · Computer Science 2021-10-06 Yu Yokoi

Stable matchings have been studied extensively in social choice literature. The focus has been mostly on integral matchings, in which the nodes on the two sides are wholly matched. A fractional matching, which is a convex combination of…

Computer Science and Game Theory · Computer Science 2022-04-20 Shivika Narang , Y Narahari

In 1962, Gale and Shapley \cite{GS} introduced the concept of stable marriages and proved their existence. Since then, the statement of the stability problem has been highly generalized. And a lot of proofs has emerged for the existence in…

Theoretical Economics · Economics 2025-05-20 V. I. Danilov

We consider stable and popular matching problems in arbitrary graphs, which are referred to as stable roommates instances. We extend the 3/2-approximation algorithm for the maximum size weakly stable matching problem to the roommates case,…

Data Structures and Algorithms · Computer Science 2025-10-07 Gergely Csáji

An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…

Discrete Mathematics · Computer Science 2021-05-21 Changyong Hu , Vijay K. Garg

This research paper emphasizes that the Stable Matching problems are the same as the problems of stable configurations of Multi-stage Interconnection Networks (MIN). The authors have solved the Stability Problem of Existing Regular Gamma…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-02-06 Ravi Rastogi , Nitin , Durg Singh Chauhan , Mahesh Chandra Govil

In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test…

Computer Science and Game Theory · Computer Science 2012-01-04 Haris Aziz , Markus Brill , Paul Harrenstein

We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a…

Computer Science and Game Theory · Computer Science 2021-05-18 Jiehua Chen , Adrian Chmurovic , Fabian Jogl , Manuel Sorge

We consider a model of stable edge sets (``matchings'') in a bipartite graph $G=(V,E)$ in which the preferences for vertices of one side (``firms'') are given via choice functions subject to standard axioms of consistency, substitutability…

Combinatorics · Mathematics 2025-01-28 Alexander V. Karzanov

Stable matching in a community consisting of $N$ men and $N$ women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and…

Computer Science and Game Theory · Computer Science 2020-05-19 Simon Mauras

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.,…

Data Structures and Algorithms · Computer Science 2024-11-04 Telikepalli Kavitha , Kazuhisa Makino

We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some natural number k, is undecidable. For the important class of…

Logic · Mathematics 2025-10-07 Manuel Bodirsky , Simon Knäuer