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Related papers: Improved Paths to Stability for the Stable Marriag…

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The stable marriage (SM) problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. In the classical formulation, n…

Artificial Intelligence · Computer Science 2010-07-07 M. Gelain , M. S. Pini , F. Rossi , K. B. Venable , T. Walsh

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

We present an n-ary constraint for the stable marriage problem. This constraint acts between two sets of integer variables where the domains of those variables represent preferences. Our constraint enforces stability and disallows bigamy.…

Data Structures and Algorithms · Computer Science 2013-08-02 Chris Unsworth , Patrick Prosser

We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the…

Data Structures and Algorithms · Computer Science 2020-09-14 Frances Cooper , David Manlove

We apply Lattice-Linear Predicate Detection Technique to derive parallel and distributed algorithms for various variants of the stable matching problem. These problems are: (a) the constrained stable marriage problem (b) the super stable…

Data Structures and Algorithms · Computer Science 2022-08-03 Vijay K. Garg

We show how fragile stable matchings are in a decentralized one-to-one matching setting. The classical work of Roth and Vande Vate (1990) suggests simple decentralized dynamics in which randomly-chosen blocking pairs match successively.…

Theoretical Economics · Economics 2024-03-20 Kirill Rudov

The Balanced Stable Marriage problem is a central optimization version of the classic Stable Marriage problem. Here, the output cannot be an arbitrary stable matching, but one that balances between the dissatisfaction of the two parties,…

Data Structures and Algorithms · Computer Science 2017-08-01 Sushmita Gupta , Sanjukta Roy , Saket Saurabh , Meirav Zehavi

We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an…

Computer Science and Game Theory · Computer Science 2016-06-29 Varun Kanade , Nikos Leonardos , Frédéric Magniez

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

Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's right -- your path to coupled life isn't through Tinder: it's…

Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…

Combinatorics · Mathematics 2017-07-25 Boris Pittel

In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…

Computer Science and Game Theory · Computer Science 2024-01-08 Naoyuki Kamiyama

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…

Artificial Intelligence · Computer Science 2017-10-30 Begum Genc , Mohamed Siala , Barry O'Sullivan , Gilles Simonin

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

An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…

Data Structures and Algorithms · Computer Science 2015-06-03 Pratik Ghosal , Adam Kunysz , Katarzyna Paluch

We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…

Data Structures and Algorithms · Computer Science 2018-12-17 Tung Mai , Vijay V. Vazirani

Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…

Combinatorics · Mathematics 2024-06-18 Boris Pittel

Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We…

Computational Complexity · Computer Science 2022-04-08 Begum Genc , Mohamed Siala , Gilles Simonin , Barry O'Sullivan

In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine…

We study the Reaching Stable Marriage via Divorces (DivorceSM) problem of deciding, given a Stable Marriage instance and an initial matching $M$ , whether there exists a stable matching which is reachable from $M$ by divorce operations as…

Computer Science and Game Theory · Computer Science 2021-02-23 Jiehua Chen