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Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

Statistics Theory · Mathematics 2026-01-21 Abhinav Chakraborty , Yuetian Luo , Rina Foygel Barber

In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…

Discrete Mathematics · Computer Science 2019-07-25 Ágnes Cseh , Klaus Heeger

We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…

Machine Learning · Computer Science 2014-09-01 Shalev Ben-David , Lev Reyzin

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 consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…

Computer Science and Game Theory · Computer Science 2022-09-08 Naoyuki Kamiyama

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…

Computer Science and Game Theory · Computer Science 2018-12-14 Kitty Meeks , Baharak Rastegari

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…

Multiagent Systems · Computer Science 2018-01-10 Jiehua Chen , Rolf Niedermeier , Piotr Skowron

The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…

Computer Science and Game Theory · Computer Science 2022-04-29 Kristóf Bérczi , Gergely Csáji , Tamás Király

It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems,…

Machine Learning · Computer Science 2018-11-29 Pascal Kerschke , Holger H. Hoos , Frank Neumann , Heike Trautmann

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…

Artificial Intelligence · Computer Science 2016-11-25 Maria Silvia Pini , Francesca Rossi , Brent Venable , Toby Walsh

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

Optimization and Control · Mathematics 2022-01-14 Marc Goerigk , Mohammad Khosravi

To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition…

Machine Learning · Statistics 2020-11-16 Hunter Lang , David Sontag , Aravindan Vijayaraghavan

Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…

Computational Complexity · Computer Science 2026-04-21 Mircea-Adrian Digulescu

An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various…

Quantum Physics · Physics 2023-07-24 Puya Mirkarimi , Adam Callison , Lewis Light , Nicholas Chancellor , Viv Kendon

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in R^{n x n} are stable. In particular, we are interested whether there exist…

Optimization and Control · Mathematics 2009-01-15 L. Gurvits , A. Olshevsky

In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…

Computer Science and Game Theory · Computer Science 2026-01-19 Naoyuki Kamiyama

While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…

Optimization and Control · Mathematics 2019-02-11 Marc Goerigk , Stephen J. Maher

Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…

Computational Complexity · Computer Science 2025-10-03 Tamás Fleiner , Zsuzsanna Jankó , Ildikó Schlotter , Alexander Teytelboym

We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated…

Formal Languages and Automata Theory · Computer Science 2017-03-01 Joel D. Day , Florin Manea , Dirk Nowotka

We study a variant of the Student-Project Allocation problem with lecturer preferences over Students where ties are allowed in the preference lists of students and lecturers (SPA-ST). We investigate the concept of strong stability in this…

Data Structures and Algorithms · Computer Science 2019-11-26 Sofiat Olaosebikan , David Manlove