Related papers: Statistical-computational gap in multiple Gaussian…
In this paper, we study the {\sc Dominating Set} problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of $p$, where $p$ is a positive constant less than $1$. We show that, given a…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
In this work, we propose an efficient two-stage algorithm solving a joint problem of correlation detection and partial alignment recovery between two Gaussian databases. Correlation detection is a hypothesis testing problem; under the null…
Network complexity, network information content analysis, and lossless compressibility of graph representations have been played an important role in network analysis and network modeling. As multidimensional networks, such as time-varying,…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…
The symmetric binary perceptron ($\texttt{SBP}$) exhibits a dramatic statistical-to-computational gap: the densities at which known efficient algorithms find solutions are far below the threshold for the existence of solutions. Furthermore,…
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results…
In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network $\mathcal{M}$ on a graph with $n$ discrete variables and bounded in-degree and bounded `confounded…
We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…
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…
We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
An open problem in graphical Gaussian models is to determine the smallest number of observations needed to guarantee the existence of the maximum likelihood estimator of the covariance matrix with probability one. In this paper we formalize…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…