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Consider an Erd\"os-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely connected subgraph). We consider the problem of…

Probability · Mathematics 2013-04-29 Yash Deshpande , Andrea Montanari

The problem of finding the largest induced balanced bipartite subgraph in a given graph is NP-hard. This problem is closely related to the problem of finding the smallest Odd Cycle Transversal. In this work, we consider the following model…

Data Structures and Algorithms · Computer Science 2022-05-16 Akash Kumar , Anand Louis , Rameesh Paul

We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…

Data Structures and Algorithms · Computer Science 2026-03-03 Alexander Morgan , Chenghao Guo

The Graph Reconstruction Conjecture famously posits that any undirected graph on at least three vertices is determined up to isomorphism by its family of (unlabeled) induced subgraphs. At present, the conjecture admits partial resolutions…

Discrete Mathematics · Computer Science 2025-12-03 Julian Asilis , Xi Chen , Dutch Hansen , Shang-Hua Teng

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s…

Machine Learning · Computer Science 2020-08-11 Sam Cole , Yizhe Zhu

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

In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…

Machine Learning · Computer Science 2018-12-03 Hendrik Fichtenberger , Dennis Rohde

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…

Data Structures and Algorithms · Computer Science 2022-07-07 Ron Kupfer , Noam Nisan

How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a…

Data Structures and Algorithms · Computer Science 2021-12-14 Claire Mathieu , Hang Zhou

Previous security research efforts orbiting around graphs have been exclusively focusing on either (de-)anonymizing the graphs or understanding the security and privacy issues of graph neural networks. Little attention has been paid to…

Machine Learning · Computer Science 2022-05-02 Yun Shen , Yufei Han , Zhikun Zhang , Min Chen , Ting Yu , Michael Backes , Yang Zhang , Gianluca Stringhini

Graph Neural Networks (GNNs) have proven to be powerful in many graph-based applications. However, they fail to generalize well under heterophilic setups, where neighbor nodes have different labels. To address this challenge, we employ a…

Machine Learning · Computer Science 2023-04-13 Yoonhyuk Choi , Jiho Choi , Taewook Ko , Chong-Kwon Kim

In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…

Machine Learning · Statistics 2025-12-30 Zhangsong Li

We analyze directed, unweighted graphs obtained from $x_i\in \mathbb{R}^d$ by connecting vertex $i$ to $j$ iff $|x_i - x_j| < \epsilon(x_i)$. Examples of such graphs include $k$-nearest neighbor graphs, where $\epsilon(x_i)$ varies from…

Machine Learning · Statistics 2014-11-24 Tatsunori B. Hashimoto , Yi Sun , Tommi S. Jaakkola

Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…

Methodology · Statistics 2025-08-08 Minsub Shin , Johan Lim , Seongoh Park

We consider a robust analog of the planted clique problem. In this analog, a set $S$ of vertices is chosen and all edges in $S$ are included; then, edges between $S$ and the rest of the graph are included with probability $\frac{1}{2}$,…

Computational Complexity · Computer Science 2018-09-06 Jacob Steinhardt

Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…

Cryptography and Security · Computer Science 2024-06-06 Dung Nguyen , Anil Vullikanti

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 investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance…

Probability · Mathematics 2026-04-10 Konstantin Avrachenkov , Andrei Bobu , Nelly Litvak , Riccardo Michielan

We study model recovery for data classification, where the training labels are generated from a one-hidden-layer neural network with sigmoid activations, also known as a single-layer feedforward network, and the goal is to recover the…

Machine Learning · Statistics 2020-05-07 Haoyu Fu , Yuejie Chi , Yingbin Liang

We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset…

Statistics Theory · Mathematics 2024-12-02 Dmitriy Kunisky , Daniel A. Spielman , Alexander S. Wein , Xifan Yu