Maximum flow and minimum-cost flow in almost-linear time

L Chen, R Kyng, YP Liu, R Peng… - 2022 IEEE 63rd …, 2022 - ieeexplore.ieee.org
We give an algorithm that computes exact maximum flows and minimum-cost flows on
directed graphs with m edges and polynomially bounded integral demands, costs, and …

Minimum cost flows, MDPs, and ℓ1-regression in nearly linear time for dense instances

J Van Den Brand, YT Lee, YP Liu, T Saranurak… - Proceedings of the 53rd …, 2021 - dl.acm.org
In this paper we provide new randomized algorithms with improved runtimes for solving
linear programs with two-sided constraints. In the special case of the minimum cost flow …

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

J Van Den Brand, L Chen, R Kyng… - 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 …

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 …

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 faster algorithm for solving general lps

S Jiang, Z Song, O Weinstein, H Zhang - Proceedings of the 53rd Annual …, 2021 - dl.acm.org
The fastest known LP solver for general (dense) linear programs is due to [Cohen, Lee and
Song'19] and runs in O*(n ω+ n 2.5− α/2+ n 2+ 1/6) time. A number of follow-up works [Lee …

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 …

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 …

Faster maxflow via improved dynamic spectral vertex sparsifiers

J van den Brand, Y Gao, A Jambulapati… - Proceedings of the 54th …, 2022 - dl.acm.org
We make several advances broadly related to the maintenance of electrical flows in
weighted graphs undergoing dynamic resistance updates, including:(1) More efficient …