We study the problem of graph clustering where the goal is to partition a graph into clusters,
ie disjoint subsets of vertices, such that each cluster is well connected internally while …

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 …

We introduce a notion for hierarchical graph clustering which we call the expander hierarchy
and show a fully dynamic algorithm for maintaining such a hierarchy on a graph with n …

We present two algorithms for dynamically maintaining a spanning forest of a graph
undergoing edge insertions and deletions. Our algorithms guarantee worst-case update …

Sketching and streaming algorithms are in the forefront of current research directions for cut
problems in graphs. In the streaming model, we show that (1--ε)-approximation for Max-Cut …

We develop a framework for graph sparsification and sketching, based on a new tool, short
cycle decomposition, which is a decomposition of an unweighted graph into an edge-disjoint …

Cut and spectral sparsification of graphs have numerous applications, including eg
speeding up algorithms for cuts and Laplacian solvers. These powerful notions have …

Graph processing has become an important part of various areas of computing, including
machine learning, medical applications, social network analysis, computational sciences …

Graph processing has become an important part of various areas of computing, including
machine learning, medical applications, social network analysis, computational sciences …

We study streaming algorithms for the fundamental geometric problem of computing the cost
of the Euclidean Minimum Spanning Tree (MST) on an n-point set X⊂ ℝ d. In the streaming …