Recent advances in fully dynamic graph algorithms–a quick reference guide

K Hanauer, M Henzinger, C Schulz - ACM Journal of Experimental …, 2022 - dl.acm.org
In recent years, significant advances have been made in the design and analysis of fully
dynamic algorithms. However, these theoretical results have received very little attention …

Fully dynamic electrical flows: Sparse maxflow faster than Goldberg–Rao

Y Gao, Y Liu, R Peng - SIAM Journal on Computing, 2023 - SIAM
We give an algorithm for computing exact maximum flows on graphs with edges and integer
capacities in the range in time. We use to suppress logarithmic factors in. For sparse graphs …

Recent advances in fully dynamic graph algorithms

K Hanauer, M Henzinger, C Schulz - arXiv preprint arXiv:2102.11169, 2021 - arxiv.org
In recent years, significant advances have been made in the design and analysis of fully
dynamic algorithms. However, these theoretical results have received very little attention …

The expander hierarchy and its applications to dynamic graph algorithms

G Goranci, H Räcke, T Saranurak, Z Tan - … of the 2021 ACM-SIAM Symposium …, 2021 - SIAM
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 …

Fast dynamic cuts, distances and effective resistances via vertex sparsifiers

L Chen, G Goranci, M Henzinger… - 2020 IEEE 61st …, 2020 - ieeexplore.ieee.org
We present a general framework of designing efficient dynamic approximate algorithms for
optimization problems on undirected graphs. In particular, we develop a technique that …

Dynamic maxflow via dynamic interior point methods

J van den Brand, YP Liu, A Sidford - Proceedings of the 55th Annual …, 2023 - dl.acm.org
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 …

Near-optimal deterministic vertex-failure connectivity oracles

Y Long, T Saranurak - 2022 IEEE 63rd Annual Symposium on …, 2022 - ieeexplore.ieee.org
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 …

Fast deterministic fully dynamic distance approximation

J Van Den Brand, S Forster… - 2022 IEEE 63rd Annual …, 2022 - ieeexplore.ieee.org
In this paper, we develop deterministic fully dynamic algorithms for computing approximate
distances in a graph with worst-case update time guarantees. In particular, we obtain …

Vertex sparsification for edge connectivity

P Chalermsook, S Das, Y Kook, B Laekhanukit… - Proceedings of the 2021 …, 2021 - SIAM
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 …

Fully Dynamic Min-Cut of Superconstant Size in Subpolynomial Time

W Jin, X Sun, M Thorup - Proceedings of the 2024 Annual ACM-SIAM …, 2024 - SIAM
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 …