We present a general toolbox, based on new vertex sparsifiers, for designing data structures
to maintain shortest paths in graphs undergoing edge insertions and/or deletions. In …

We present a deterministic fully dynamic algorithm to answer c-edge connectivity queries on
pairs of vertices in n°(1) worst case update and query time for any positive integer c=(log …

A partition of a weighted graph is-sparse if every cluster has diameter at most, and every ball
of radius intersects at most clusters. Similarly, is-scattering if instead for balls, we require that …

We study vertex sparsification for distances, in the setting of planar graphs with distortion:
Given a planar graph G (with edge weights) and a subset of k terminal vertices, the goal is to …

A partition $\mathcal {P} $ of a weighted graph $ G $ is $(\sigma,\tau,\Delta) $-sparse if every
cluster has diameter at most $\Delta $, and every ball of radius $\Delta/\sigma $ intersects at …

Graph compression or sparsification is a basic information-theoretic and computational
question. A major open problem in this research area is whether (1+∊)-approximate cut …

We introduce a new approach to spectral sparsification that approximates the quadratic form
of the pseudoinverse of a graph Laplacian restricted to a subspace. We show that sparsifiers …

We study the following version of cut sparsification. Given a large edge-weighted network G
with k terminal vertices, compress it into a smaller network H with the same terminals, such …

Given a large edge-capacitated network G and a subset of k vertices called terminals, an
(exact) flow sparsifier is a small network G'that preserves (exactly) all multicommodity flows …

Given a large graph G with a subset| T|= k of its vertices called terminals, a quality-q flow
sparsifier is a small graph G'that contains T and preserves all multicommodity flows that can …