相关论文: Sharp threshold for network recovery from voter mo…
The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
We study the problem of reconstructing the latent geometry of a $d$-dimensional Riemannian manifold from a random geometric graph. While recent works have made significant progress in manifold recovery from random geometric graphs, and more…
In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erd\"os-R\'enyi graphs with connection probability given by $\lambda/n^\alpha$ (with…
A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most…
We study the voter dynamics model on heterogeneous graphs. We exploit the non-conservation of the magnetization to characterize how consensus is reached on networks with different connectivity patterns. For a network of N sites with an…
Given an arbitrary subgraph $H=H_n$ and $p=p_n \in (0,1)$, the planted subgraph model is defined as follows. A statistician observes the union a random copy $H^*$ of $H$, together with random noise in the form of an instance of an…
We consider the problem of exact recovery of any $m\times n$ matrix of rank $\varrho$ from a small number of observed entries via the standard nuclear norm minimization framework. Such low-rank matrices have degrees of freedom $(m+n)\varrho…
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…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
The approximate period recovery problem asks to compute all $\textit{approximate word-periods}$ of a given word $S$ of length $n$: all primitive words $P$ ($|P|=p$) which have a periodic extension at edit distance smaller than $\tau_p$ from…
Motivated by the problem of matching two correlated random geometric graphs, we study the problem of matching two Gaussian geometric models correlated through a latent node permutation. Specifically, given an unknown permutation $\pi^*$ on…
The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands…
The problems of detecting and recovering planted structures/subgraphs in Erd\H{o}s-R\'{e}nyi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques.…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…