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Related papers: Exact recovery for seeded graph matching

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In this paper, we study the problem of exact community recovery in the symmetric stochastic block model, where a graph of $n$ vertices is randomly generated by partitioning the vertices into $K \ge 2$ equal-sized communities and then…

Optimization and Control · Mathematics 2021-06-11 Peng Wang , Huikang Liu , Zirui Zhou , Anthony Man-Cho So

Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of…

Machine Learning · Statistics 2018-01-17 Bruce Hajek , Yihong Wu , Jiaming Xu

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

Data Structures and Algorithms · Computer Science 2015-04-30 Vitaly Feldman , Will Perkins , Santosh Vempala

Many models for undirected graphs are based on factorizing the graph's adjacency matrix; these models find a vector representation of each node such that the predicted probability of a link between two nodes increases with the similarity…

Machine Learning · Computer Science 2022-10-04 Sudhanshu Chanpuriya , Ryan A. Rossi , Anup Rao , Tung Mai , Nedim Lipka , Zhao Song , Cameron Musco

Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…

Information Theory · Computer Science 2019-04-04 Mengnan Zhao , M. Devrim Kaba , René Vidal , Daniel P. Robinson , Enrique Mallada

In an undirected graph $G=(V,E)$, we say $(A,B)$ is a pair of perfectly matched sets if $A$ and $B$ are disjoint subsets of $V$ and every vertex in $A$ (resp. $B$) has exactly one neighbor in $B$ (resp. $A$). The size of a pair of perfectly…

Discrete Mathematics · Computer Science 2022-11-08 N. R. Aravind , Roopam Saxena

We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…

Signal Processing · Electrical Eng. & Systems 2024-09-19 Chang Ye , Gonzalo Mateos

The planted bisection model is a random graph model in which the nodes are divided into two equal-sized communities and then edges are added randomly in a way that depends on the community membership. We establish necessary and sufficient…

Probability · Mathematics 2020-07-14 Elchanan Mossel , Joe Neeman , Allan Sly

Most recent developments on the stochastic block model (SBM) rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet…

Probability · Mathematics 2015-06-12 Emmanuel Abbe , Colin Sandon

The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…

Computational Complexity · Computer Science 2025-07-08 Nikhil S. Mande , Swagato Sanyal , Viktor Zamaraev

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

Combinatorics · Mathematics 2022-02-21 Pu Gao , Calum MacRury , Pawel Pralat

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 the \emph{graph matching} problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair…

Statistics Theory · Mathematics 2024-05-07 Ernesto Araya , Guillaume Braun , Hemant Tyagi

We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…

Data Structures and Algorithms · Computer Science 2020-12-01 Amit Levi , Ramesh Krishnan S. Pallavoor , Sofya Raskhodnikova , Nithin Varma

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Information Theory · Computer Science 2015-03-20 Meng Wang , Weiyu Xu , Enrique Mallada , Ao Tang

The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community…

Optimization and Control · Mathematics 2022-05-13 Alberto Del Pia , Aida Khajavirad , Dmitriy Kunisky

Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…

Computational Geometry · Computer Science 2022-05-18 Varsha Dani , Josep Díaz , Thomas P. Hayes , Cristopher Moore

We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…

Data Structures and Algorithms · Computer Science 2015-07-10 Naman Agarwal , Afonso S. Bandeira , Konstantinos Koiliaris , Alexandra Kolla

The stochastic block model (SBM) is an important generative model for random graphs in network science and machine learning, useful for benchmarking community detection (or clustering) algorithms. The symmetric SBM generates a graph with…

Machine Learning · Computer Science 2016-11-17 Akshay Gadde , Eyal En Gad , Salman Avestimehr , Antonio Ortega

A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the…

Social and Information Networks · Computer Science 2018-05-04 Austin R. Benson , Jon Kleinberg