Many real-world datasets can be naturally represented as graphs, spanning a wide range of
domains. However, the increasing complexity and size of graph datasets present significant …

For a class F of complex-valued functions on a set D, we denote by gn (F) its sampling
numbers, ie, the minimal worst-case error on F, measured in L 2, that can be achieved with a …

As large-scale graphs become increasingly more prevalent, it poses significant
computational challenges to process, extract and analyze large graph data. Graph …

We prove, using the subspace embedding guarantee in a black box way, that one can
achieve the spectral norm guarantee for approximate matrix multiplication with a …

In this paper we provide an algorithm which given any m-edge n-vertex directed graph with
integer capacities at most U computes a maximum st flow for any vertices s and t in m 11/8+ …

We present a general framework for constructing cut sparsifiers in undirected graphs---
weighted subgraphs for which every cut has the same weight as the original graph, up to a …

In this paper 1, we study matrix scaling and balancing, which are fundamental problems in
scientific computing, with a long line of work on them that dates back to the 1960s. We …

In this paper, we begin to address the longstanding algorithmic gap between general and
reversible Markov chains. We develop directed analogues of several spectral graph …

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 …

In the age of Big Data, efficient algorithms are now in higher demand more than ever before.
While Big Data takes us into the asymptotic world envisioned by our pioneers, it also …