We consider a fundamental algorithmic question in spectral graph theory: Compute a
spectral sparsifier of random-walk matrix-polynomial $$ L_\alpha (G)= D-\sum_ {r= 1} …

For" large" class $\mathcal {C} $ of continuous probability density functions (pdf), we
demonstrate that for every $ w\in\mathcal {C} $ there is mixture of discrete Binomial …

Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale
networks by reducing the overall number of edges, while maintaining a comparable graph …

We present three spectral sparsification algorithms that, on input a graph G with n vertices
and m edges, return a graph H with n vertices and O (n log n/epsilon^ 2) edges that provides …

We study algorithms for spectral graph sparsification. The input is a graph G with n vertices
and m edges, and the output is a sparse graph G̃ that approximates G in an algebraic sense …

For any undirected and weighted graph G=(V, E, w) with n vertices and m edges, we call a
sparse subgraph H of G, with proper reweighting of the edges, a (1+ ε)-spectral sparsifier if …

A sparsifier of a graph is a sparse graph that approximates it. A spectral sparsifier is one that
approximates it spectrally, which means that their Laplacian matrices have similar quadratic …

Motivated by a sampling problem basic to computational statistical inference, we develop a
nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical …

Given a matrix A\in R^{mxn}, we present a randomized algorithm that sparsifies A by
retaining some of its elements by sampling them according to a distribution that depends on …

In this paper, we introduce a new, spectral notion of approximation between directed graphs,
which we call singular value (SV) approximation. SV-approximation is stronger than …