We present a general framework of designing efficient dynamic approximate algorithms for
optimization problems on undirected graphs. In particular, we develop a technique that …

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 …

We revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph
data structure problems under vertex updates, yet its complexity is still not well-understood …

We study distributed algorithms built around minor-based vertex sparsifiers, and give the first
algorithm in the CONGEST model for solving linear systems in graph Laplacian matrices to …

We present a deterministic fully dynamic algorithm with subpolynomial worst-case time per
graph update such that after processing each update of the graph, the algorithm outputs a …

In this article, we show that the algorithm of maintaining expander decompositions in graphs
undergoing edge deletions directly by removing sparse cuts repeatedly can be made …

This paper extends and generalizes the well-known cut-matching game framework and
provides a novel cut-strategy that produces constant-hop expanders. Constant-hop …

In the vertex connectivity problem, given an undirected n-vertex m-edge graph G, we need to
compute the minimum number of vertices that can disconnect G after removing them. This …

We provide an algorithm which, with high probability, maintains a (1—ɛ)-approximate
maximum flow on an undirected graph undergoing m-edge additions in amortized mo (1) ɛ …

In this work, we present the first algorithm to compute expander decompositions in an $ m $-
edge directed graph with near-optimal time $\tilde {O}(m) $. Further, our algorithm can …