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In the stable marriage problem (SM), a mechanism that always outputs a stable matching is called a stable mechanism. One of the well-known stable mechanisms is the man-oriented Gale-Shapley algorithm (MGS). MGS has a good property that it…

Computer Science and Game Theory · Computer Science 2019-02-18 Koki Hamada , Shuichi Miyazaki , Hiroki Yanagisawa

In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for…

Data Structures and Algorithms · Computer Science 2025-01-23 Itai Ashlagi , Jiale Chen , Mohammad Roghani , Amin Saberi

The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical…

Computer Science and Game Theory · Computer Science 2016-03-21 Baharak Rastegari , Paul Goldberg , David Manlove

The study of marriage dynamics and of strategies to reduce the likelihood of divorce has been an important research area for many years. Gottman's research on successful marriages revealed three matched interaction styles:…

Optimization and Control · Mathematics 2024-06-12 Micah Henson , Mark Kot , Ka-Kit Tung

The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly…

Computer Science and Game Theory · Computer Science 2026-02-25 Moshe Babaioff , Rotem Gil , Assaf Romm

Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a…

Computer Science and Game Theory · Computer Science 2018-07-19 Itai Ashlagi , Yannai A. Gonczarowski

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

The research paper emphasizes that the Stable Matching problems are the same as the problems of stable configurations of Multi-stage Interconnection Networks (MIN). We have discusses the Stability Problems of Existing Regular Omega…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-02-07 Ravi Rastogi , Nitin , Durg Singh Chauhan , Mahesh Chandra Govil

The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…

Computational Complexity · Computer Science 2018-02-21 Jiehua Chen , Danny Hermelin , Manuel Sorge , Harel Yedidsion

We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…

Computer Science and Game Theory · Computer Science 2020-12-25 Ioannis Caragiannis , Aris Filos-Ratsikas , Panagiotis Kanellopoulos , Rohit Vaish

This paper is concerned with the popular Sudoku problem. We proposed a warm restart strategy for solving Sudoku puzzles, based on the sparse optimization technique. Furthermore, we defined a new difficulty level for Sudoku puzzles. The…

Optimization and Control · Mathematics 2018-03-16 Yuchao Tang , Zhenggang Wu , Chuanxi Zhu

Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…

Combinatorics · Mathematics 2026-01-13 Byron Chin , Marcus Michelen

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

Optimization and Control · Mathematics 2017-01-03 Dongcai Su

The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…

Data Structures and Algorithms · Computer Science 2014-11-26 Ágnes Cseh , Brian C. Dean

We study stability notions for networked many-to-many matching markets with individually insignificant agents in distributional form. Outcomes are formulated as joint distributions over characteristics of agents and contract choices.…

Theoretical Economics · Economics 2026-05-01 Michael Greinecker , Karolina Vocke

A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…

Data Structures and Algorithms · Computer Science 2020-07-20 Kohei Nishikawa , Takahisa Toda

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

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 this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…

Computer Science and Game Theory · Computer Science 2025-02-11 Gergely Csáji

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…

Computer Science and Game Theory · Computer Science 2025-01-23 Zhaohong Sun , Tomohiko Yokoyama , Makoto Yokoo