English
Related papers

Related papers: Matching in Stochastically Evolving Graphs

200 papers

We investigate online maximum cardinality matching, a central problem in ad allocation. In this problem, users are revealed sequentially, and each new user can be paired with any previously unmatched campaign that it is compatible with.…

Data Structures and Algorithms · Computer Science 2024-10-28 Flore Sentenac , Nathan Noiry , Matthieu Lerasle , Laurent Ménard , Vianney Perchet

We present an algorithm that finds a maximum cardinality $f$-matching of a simple graph in time $O(n^{2/3} m)$. Here $f:V\to \mathbb{N}$ is a given function, and an $f$-matching is a subgraph wherein each vertex $v\in V$ has degree $\le…

Data Structures and Algorithms · Computer Science 2023-11-27 Harold Gabow

We study online algorithms for maximum cardinality matchings with edge arrivals in graphs of low degree. Buchbinder, Segev, and Tkach showed that no online algorithm for maximum cardinality fractional matchings can achieve a competitive…

Data Structures and Algorithms · Computer Science 2026-02-10 Kanstantsin Pashkovich , Thomas Snow

This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…

Combinatorics · Mathematics 2023-01-24 Péter Madarasi

We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming fashion. We analyze a variant of the previously best-known…

Data Structures and Algorithms · Computer Science 2018-05-01 Elena Grigorescu , Morteza Monemizadeh , Samson Zhou

We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and…

Computer Science and Game Theory · Computer Science 2021-06-15 Mobin Y. Jeloudar , Irene Lo , Tristan Pollner , Amin Saberi

We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or $1$. Let…

Computational Geometry · Computer Science 2019-03-26 Nathaniel Lahn , Sharath Raghvendra

In this paper, we address the optimal control of stochastic matching models on general graphs and single arrivals having fixed arrival rates, as introduced in \cite{MaiMoy16}. On the `N-shaped' graph, by following the dynamic programming…

Optimization and Control · Mathematics 2024-02-06 Loïc Jean , Pascal Moyal

The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic $k$-set packing, where the problem is to find a maximum packing…

Data Structures and Algorithms · Computer Science 2015-04-30 Avrim Blum , John P. Dickerson , Nika Haghtalab , Ariel D. Procaccia , Tuomas Sandholm , Ankit Sharma

Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…

Machine Learning · Computer Science 2021-09-14 Linfeng Liu , Michael C. Hughes , Soha Hassoun , Li-Ping Liu

Consider a kidney-exchange application where we want to find a max-matching in a random graph. To find whether an edge $e$ exists, we need to perform an expensive test, in which case the edge $e$ appears independently with a \emph{known}…

Data Structures and Algorithms · Computer Science 2019-02-07 Domagoj Bradac , Sahil Singla , Goran Zuzic

We present a randomized algorithm to maintain a maximal matching without 3 length augmenting paths in the fully dynamic setting. Consequently, we maintain a $3/2$ approximate maximum cardinality matching. Our algorithm takes expected…

Data Structures and Algorithms · Computer Science 2018-11-06 Manas Jyoti Kashyop , N. S. Narayanaswamy

We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…

Data Structures and Algorithms · Computer Science 2018-11-09 Soheil Behnezhad , Alireza Farhadi , MohammadTaghi Hajiaghayi , Nima Reyhani

In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…

Data Structures and Algorithms · Computer Science 2022-09-09 Jan van den Brand , Sebastian Forster , Yasamin Nazari

In this paper we study the classic problem of computing a maximum cardinality matching in general graphs $G = (V, E)$. The best known algorithm for this problem till date runs in $O(m \sqrt{n})$ time due to Micali and Vazirani \cite{MV80}.…

Data Structures and Algorithms · Computer Science 2011-08-18 Anant Jindal , Gazal Kochar , Manjish Pal

Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…

Machine Learning · Statistics 2020-07-06 Jesús Arroyo , Daniel L. Sussman , Carey E. Priebe , Vince Lyzinski

A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a…

Discrete Mathematics · Computer Science 2020-09-11 Arnaud Cadas , Ana Bušić , Josu Doncel

Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…

Machine Learning · Statistics 2020-07-21 Jian Ding , Zongming Ma , Yihong Wu , Jiaming Xu

Consider the following stochastic matching problem. Given a graph $G=(V, E)$, an unknown subgraph $G_p = (V, E_p)$ is realized where $E_p$ includes every edge of $E$ independently with some probability $p \in (0, 1]$. The goal is to query a…

Data Structures and Algorithms · Computer Science 2025-06-25 Amir Azarmehr , Soheil Behnezhad , Alma Ghafari , Ronitt Rubinfeld

We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…

Data Structures and Algorithms · Computer Science 2017-04-28 Zengfeng Huang , Bozidar Radunovic , Milan Vojnovic , Qin Zhang