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We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…

Data Structures and Algorithms · Computer Science 2019-02-01 Boaz Barak , Chi-Ning Chou , Zhixian Lei , Tselil Schramm , Yueqi Sheng

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 study the problem of robustly estimating the edge density of Erd\H{o}s-R\'enyi random graphs $G(n, d^\circ/n)$ when an adversary can arbitrarily add or remove edges incident to an $\eta$-fraction of the nodes. We develop the first…

Data Structures and Algorithms · Computer Science 2025-03-07 Hongjie Chen , Jingqiu Ding , Yiding Hua , Stefan Tiegel

In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…

Statistics Theory · Mathematics 2017-03-16 Yohann De Castro , Thibault Espinasse , Paul Rochet

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the…

Signal Processing · Electrical Eng. & Systems 2023-08-15 Jhon A. Castro-Correa , Jhony H. Giraldo , Anindya Mondal , Mohsen Badiey , Thierry Bouwmans , Fragkiskos D. Malliaros

Expander graphs are known to be robust to edge deletions in the following sense: for any online sequence of edge deletions $e_1, e_2, \ldots, e_k$ to an $m$-edge graph $G$ that is initially a $\phi$-expander, the algorithm can grow a set $P…

Data Structures and Algorithms · Computer Science 2025-04-02 Simon Meierhans , Maximilian Probst Gutenberg , Thatchaphol Saranurak

Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…

Probability · Mathematics 2025-11-10 Han Huang , Pakawut Jiradilok , Elchanan Mossel

A variety of information processing tasks in practice involve recovering $n$ objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph $\mathcal{G}$. This paper concerns the…

Information Theory · Computer Science 2016-08-04 Yuxin Chen , Andrea J. Goldsmith

We estimate the minimum number of distance queries that is sufficient to reconstruct the binomial random graph $G(n,p)$ with constant diameter with high probability. We get a tight (up to a constant factor) answer for all $p>n^{-1+o(1)}$…

Combinatorics · Mathematics 2024-07-31 Michael Krivelevich , Maksim Zhukovskii

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…

Data Structures and Algorithms · Computer Science 2024-06-12 Ziao Wang , Weina Wang , Lele Wang

Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models…

Information Theory · Computer Science 2019-05-02 Luca Corinzia , Paolo Penna , Luca Mondada , Joachim M. Buhmann

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

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…

Statistics Theory · Mathematics 2021-02-18 Antoine Maillard , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…

Combinatorics · Mathematics 2019-07-30 Michael Anastos , Peleg Michaeli , Samantha Petti

Random graph alignment refers to recovering the underlying vertex correspondence between two random graphs with correlated edges. This can be viewed as an average-case and noisy version of the well-known graph isomorphism problem. For the…

Machine Learning · Statistics 2021-08-18 Luca Ganassali , Laurent Massoulié , Marc Lelarge

Matrix-variate Gaussian graphical models (GGM) have been widely used for modeling matrix-variate data. Since the support of sparse precision matrix represents the conditional independence graph among matrix entries, conducting support…

Methodology · Statistics 2017-09-01 Xi Chen , Weidong Liu

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…

Data Structures and Algorithms · Computer Science 2016-12-13 Monika Henzinger , Sebastian Krinninger , Danupon Nanongkai

The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution…

Machine Learning · Computer Science 2024-02-20 Emmanuel Esposito , Federico Fusco , Dirk van der Hoeven , Nicolò Cesa-Bianchi

In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on the message complexity. We provide an algorithm that solves the implicit version of leader election (where…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-01-03 Seth Gilbert , Peter Robinson , Suman Sourav

We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex…

Information Theory · Computer Science 2018-05-15 Daniel Cullina , Negar Kiyavash