Recent advances in fully dynamic graph algorithms–a quick reference guide
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 …
dynamic algorithms. However, these theoretical results have received very little attention …
Fully dynamic electrical flows: Sparse maxflow faster than Goldberg–Rao
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 …
capacities in the range in time. We use to suppress logarithmic factors in. For sparse graphs …
Recent advances in fully dynamic graph algorithms
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 …
dynamic algorithms. However, these theoretical results have received very little attention …
The expander hierarchy and its applications to dynamic graph algorithms
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 …
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
We present a general framework of designing efficient dynamic approximate algorithms for
optimization problems on undirected graphs. In particular, we develop a technique that …
optimization problems on undirected graphs. In particular, we develop a technique that …
Dynamic maxflow via dynamic interior point methods
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 …
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 …
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 …
distances in a graph with worst-case update time guarantees. In particular, we obtain …
Vertex sparsification for edge connectivity
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 …
question. A major open problem in this research area is whether (1+∊)-approximate cut …
Fully Dynamic Min-Cut of Superconstant Size in Subpolynomial Time
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 …
graph update such that after processing each update of the graph, the algorithm outputs a …