Let G=(V, E, w) be a weighted, directed graph subject to a sequence of adversarial edge
deletions. In the decremental single-source reachability problem (SSR), we are given a fixed …

In the decremental single-source shortest paths problem, the goal is to maintain distances
from a fixed source s to every vertex v in an m-edge graph undergoing edge deletions. In …

Given an input that undergoes a sequence of updates, a dynamic algorithm maintains a
valid solution to some predefined problem at any point in time; the goal is to design an …

We show a fully dynamic algorithm for maintaining (1+ϵ)-approximate size of maximum
matching of the graph with n vertices and m edges using m^0.5-ϵ(1) update time. This is the …

Designing dynamic graph algorithms against an adaptive adversary is a major goal in the
field of dynamic graph algorithms. While a few such algorithms are known for spanning …

We show a fully dynamic algorithm for maintaining (1+ ϵ)-approximate size of maximum
matching of the graph with n vertices and m edges using m0. 5− Ωϵ (1) update time. This is …

We give the first almost-linear time algorithms for several problems in incremental graphs
including cycle detection, strongly connected component maintenance, st shortest path …

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 …

In the decremental Single-Source Shortest Path problem (SSSP), we are given a weighted
directed graph G=(V, E, w) undergoing edge deletions and a source vertex r∈ V; let n=| V …

In this paper we provide an algorithm for maintaining a (1− є)-approximate maximum flow in
a dynamic, capacitated graph undergoing edge insertions. Over a sequence of m insertions …