Differentially private analysis of graphs is widely used for releasing statistics from sensitive
graphs while still preserving user privacy. Most existing algorithms however are in a …

We study iterative methods based on Krylov subspaces for low-rank approximation under
any Schatten-p norm. Here, given access to a matrix A through matrix-vector products, an …

Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but
the corresponding problem of proving lower bounds for this task has remained elusive, with …

We consider the problem of rank-1 low-rank approximation (LRA) in the matrix-vector
product model under various Schatten norms: _ ‖ u ‖ _ 2= 1\left ‖ A\left (Iu u …

Matrix trace estimation is ubiquitous in machine learning applications and has traditionally
relied on Hutchinson's method, which requires $ O (\log (1/\delta)/\epsilon^ 2) $ matrix-vector …

We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up
to polylogarithmic factors in five models of computation: the two-party communication, AND …

The distance matrix of a dataset $ X $ of $ n $ points with respect to a distance function $ f $
represents all pairwise distances between points in $ X $ induced by $ f $. Due to their wide …

We study the problem of finding a spanning forest in an undirected, $ n $-vertex multi-graph
under two basic query models. One is the Linear query model which are linear …

We study the problem of testing whether a symmetric d*d input matrix A is symmetric positive
semidefinite (PSD), or is ϵ-far from the PSD cone, meaning that min(A)≦-ϵ‖Ap, where …

Let G be an n-vertex graph with m edges. When asked a subset S of vertices, a cut query on
G returns the number of edges of G that have exactly one endpoint in S. We show that there …