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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

An integer linear system is a set of inequalities with integer constraints. The solution graph of an integer linear system is an undirected graph defined on the set of feasible solutions to the integer linear system. In this graph, a pair…

Discrete Mathematics · Computer Science 2025-05-20 Takasugu Shigenobu , Naoyuki Kamiyama

In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that…

Computer Science and Game Theory · Computer Science 2010-11-12 Ankur Mani , Asuman Ozdaglar , Alex , Pentland

We investigate the Euclidean $d$-Dimensional Stable Roommates problem, which asks whether a given set~$V$ of $d \cdot n$ points from the 2-dimensional Euclidean space can be partitioned into $n$ disjoint (unordered) subsets…

Computer Science and Game Theory · Computer Science 2022-07-05 Jiehua Chen , Sanjukta Roy

The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…

Physics and Society · Physics 2018-06-26 Gui-Yuan Shi , Yi-Xiu Kong , Bo-Lun Chen , Guang-Hui Yuan , Rui-Jie Wu

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…

Theoretical Economics · Economics 2024-06-14 Gregory Gutin , Philip R. Neary , Anders Yeo

Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…

Computer Science and Game Theory · Computer Science 2012-07-17 Haris Aziz

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

This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…

Optimization and Control · Mathematics 2014-09-26 Dean Richert , Jorge Cortes

In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…

Logic in Computer Science · Computer Science 2007-05-23 Miroslaw Truszczynski

We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…

Computer Science and Game Theory · Computer Science 2016-07-12 Haris Aziz , Péter Biró , Serge Gaspers , Ronald de Haan , Nicholas Mattei , Baharak Rastegari

The maximum stable set problem is a well-known NP-hard problem in combinatorial optimization, which can be formulated as the maximization of a quadratic square-free polynomial over the (Boolean) hypercube. We investigate a hierarchy of…

Optimization and Control · Mathematics 2013-10-11 Monique Laurent , Zhao Sun

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

We propose an $O(n^2)$-time algorithm to determine whether a given matching is efficient in the roommates problem.

Computer Science and Game Theory · Computer Science 2025-03-04 Keita Kuwahara

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

Following up a recent work by Ashlagi, Kanoria and Leshno, we study a stable matching problem with unequal numbers of men and women, and independent uniform preferences. The asymptotic formulas for the expected number of stable matchings,…

Combinatorics · Mathematics 2017-02-14 Boris Pittel

Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…

Computer Science and Game Theory · Computer Science 2024-08-30 Naoyuki Kamiyama

Stability is crucial in matching markets, yet in many real-world settings - from hospital residency allocations to roommate assignments - full stability is either impossible to achieve or can come at the cost of leaving many agents…

Computer Science and Game Theory · Computer Science 2026-01-21 Frederik Glitzner , David Manlove

In a multiple partners matching problem the agents can have multiple partners up to their capacities. In this paper we consider both the two-sided many-to-many stable matching problem and the one-sided stable fixtures problem under…

Computer Science and Game Theory · Computer Science 2022-02-14 Péter Biró , Gergely Csáji

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…

Combinatorics · Mathematics 2007-05-23 W. J. van Hoeve