A deterministic almost-linear time algorithm for minimum-cost flow

J Van Den Brand, L Chen, R Peng… - 2023 IEEE 64th …, 2023 - ieeexplore.ieee.org
We give a deterministic m^1+o(1) time algorithm that computes exact maximum flows and
minimum-cost flows on directed graphs with m edges and polynomially bounded integral …

Bipartite matching in nearly-linear time on moderately dense graphs

J van den Brand, YT Lee, D Nanongkai… - 2020 IEEE 61st …, 2020 - ieeexplore.ieee.org
We present an ̃O(m+n^1.5)-time randomized algorithm for maximum cardinality bipartite
matching and related problems (eg transshipment, negative-weight shortest paths, and …

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 …

A survey on exact algorithms for the maximum flow and minimum‐cost flow problems

O Cruz‐Mejía, AN Letchford - Networks, 2023 - Wiley Online Library
Network flow problems form an important and much‐studied family of combinatorial
optimization problems, with a huge array of practical applications. Two network flow …

Unit Capacity Maxflow in Almost Time

T Kathuria, YP Liu, A Sidford - SIAM Journal on Computing, 2022 - SIAM
We present an algorithm which given any m-edge directed graph with positive integer
capacities at most U, vertices a and b, and an approximation parameter ϵ∈(0,1) computes …

Deterministic decremental reachability, scc, and shortest paths via directed expanders and congestion balancing

A Bernstein, MP Gutenberg… - 2020 IEEE 61st Annual …, 2020 - ieeexplore.ieee.org
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 …

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 …

Negative-weight single-source shortest paths in near-linear time

A Bernstein, D Nanongkai… - 2022 IEEE 63rd annual …, 2022 - ieeexplore.ieee.org
We present a randomized algorithm that computes single-source shortest paths (SSSP) in
O\left(m\log^8(n)\logW\right) time when edge weights are integral and can be negative. 1 …

Dynamic algorithms against an adaptive adversary: generic constructions and lower bounds

A Beimel, H Kaplan, Y Mansour, K Nissim… - Proceedings of the 54th …, 2022 - dl.acm.org
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 …

Deterministic min-cut in poly-logarithmic max-flows

J Li, D Panigrahi - 2020 IEEE 61st Annual Symposium on …, 2020 - ieeexplore.ieee.org
We give a deterministic (global) min-cut algorithm for weighted undirected graphs that runs
in time O (m 1+ ε) plus polylog (n) max-flow computations. Using the current best max-flow …