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Related papers: Computational complexity of $k$-stable matchings

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We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable…

Computer Science and Game Theory · Computer Science 2021-08-23 Niclas Boehmer , Robert Bredereck , Klaus Heeger , Rolf Niedermeier

This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a…

Theoretical Economics · Economics 2025-07-11 Shashwat Khare , Souvik Roy , Ton Storcken

In the Stable Marriage Problem two sets of agents must be paired according to mutual preferences, which may happen to conflict. We present two generalizations of its sex-oriented version, aiming to take into account correlations between the…

Disordered Systems and Neural Networks · Physics 2009-11-07 G. Caldarelli , Andrea Capocci , Paolo Laureti

Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…

Data Structures and Algorithms · Computer Science 2015-01-26 Katarina Cechlarova , Tamas Fleiner , David F. Manlove , Iain McBride

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…

Computer Science and Game Theory · Computer Science 2014-09-16 Martin Hoefer , Lisa Wagner

Since the early days of research in algorithms and complexity, the computation of stable matchings is a core topic. While in the classic setting the goal is to match up two agents (either from different "gender" (this is Stable Marriage) or…

Computational Complexity · Computer Science 2021-04-02 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…

Probability · Mathematics 2024-01-01 Christopher Hoffman , Avi Levy , Elchanan Mossel

Stable matching in a community consisting of men and 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 Shapley, who…

Data Structures and Algorithms · Computer Science 2021-12-14 Hugo Gimbert , Claire Mathieu , Simon Mauras

We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…

Condensed Matter · Physics 2009-10-30 M. J. Omero , M. Dzierzawa , M. Marsili , Y. -C. Zhang

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…

Computer Science and Game Theory · Computer Science 2025-06-06 Gergely Csáji

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…

Statistical Mechanics · Physics 2009-10-31 G. Caldarelli , A. Capocci

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…

Computer Science and Game Theory · Computer Science 2021-12-14 Niclas Boehmer , Klaus Heeger , Rolf Niedermeier

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…

Discrete Mathematics · Computer Science 2021-06-10 Agnes Cseh , Yuri Faenza , Telikepalli Kavitha , Vladlena Powers

We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances…

Computational Complexity · Computer Science 2012-04-20 Prasad Chebolu , Leslie Ann Goldberg , Russell Martin

We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…

Computer Science and Game Theory · Computer Science 2026-01-14 Rohith Reddy Gangam , Tung Mai , Nitya Raju , 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

Suppose that each member of a set of agents has a preference list of a subset of houses, possibly involving ties and each agent and house has their capacity denoting the maximum number of correspondingly agents/houses that can be matched to…

Data Structures and Algorithms · Computer Science 2011-01-04 Katarzyna Paluch

We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…

Computer Science and Game Theory · Computer Science 2018-10-09 Vijay Menon , Kate Larson

We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…

Theoretical Economics · Economics 2025-07-11 Shashwat Khare , Souvik Roy

Given $n$ men, $n$ women, and $n$ dogs, each man has an incomplete preference list of women, each woman does an incomplete preference list of dogs, and each dog does an incomplete preference list of men. We understand a family as a triple…

Combinatorics · Mathematics 2021-07-22 E. Yu. Lerner , R. E. Lerner