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A large body of work has been devoted to defining and identifying clusters or communities in
social and information networks, ie, in graphs in which the nodes represent underlying …

Algorithms in varied fields use the idea of maintaining a distribution over a certain set and
use the multiplicative update rule to iteratively change these weights. Their analyses are …

A large body of work has been devoted to identifying community structure in networks. A
community is often though of as a set of nodes that has more connections between its …

We give a O (√ log n)-approximation algorithm for the sparsest cut, edge expansion,
balanced separator, and graph conductance problems. This improves the O (log n) …

We consider the classical Minimum Balanced Cut problem: given a graph G, compute a
partition of its vertices into two subsets of roughly equal volume, while minimizing the …

Spectral graph theory is the study and exploration of graphs through the eigenvalues and
eigenvectors of matrices naturally associated with those graphs. It is intuitively related to …

We study the design of local algorithms for massive graphs. A local graph algorithm is one
that finds a solution containing or near a given vertex without looking at the whole graph. We …

The ability to solve a system of linear equations lies at the heart of areas such as
optimization, scientific computing, and computer science, and has traditionally been a …

Semidefinite programs (SDP) have been used in many recentapproximation algorithms. We
develop a general primal-dualapproach to solve SDPs using a generalization ofthe well …