# Faster Sparse Minimum Cost Flow by Electrical Flow Localization

@article{Axiotis2022FasterSM, title={Faster Sparse Minimum Cost Flow by Electrical Flow Localization}, author={Kyriakos Axiotis and Aleksander Mkadry and Adrian Vladu}, journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)}, year={2022}, pages={528-539} }

We give an $\tilde{O}(m^{3/2-1/762}\log(U+W))$ time algorithm for minimum cost flow with capacities bounded by $U$ and costs bounded by $W$. For sparse graphs with general capacities, this is the first algorithm to improve over the $\tilde{O}(m^{3/2}\log^{O(1)}(U+W))$ running time obtained by an appropriate instantiation of an interior point method [Daitch-Spielman, 2008]. Our approach is extending the framework put forth in [Gao-Liu-Peng, 2021] for computing the maximum flow in graphs with…

## 4 Citations

Faster Maxflow via Improved Dynamic Spectral Vertex Sparsifiers

- Computer ScienceArXiv
- 2021

This work proposes an algorithm that on graphs with m edges computes a mincost flow with edge costs and capacities in [1, U ] in time Õ(m log U) time maxflow, improving over the â‚¬(mlog U)Time maxflow algorithm of [Gao-Liu-Peng FOCS 2021].

Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time

- Computer ScienceArXiv
- 2021

This work proposes a framework that uses m cost only in the initialization phase and achieves a truly subquadratic cost per iteration in terms of m, i.e., m per iteration, and makes use of various techniques, including a shifted ReLU-based sparsifier, a lazy low rank maintenance data structure, fast rectangular matrix multiplication, tensor-based sketching techniques and preconditioning.

The Laplacian Paradigm in the Broadcast Congested Clique

- Computer Science
- 2022

In this paper, we bring the main tools of the Laplacian paradigm to the Broadcast Congested Clique. We introduce an algorithm to compute spectral sparsiers in a polylogarithmic number of rounds,…

Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts

- Computer Science
- 2021

A hybrid communication model which enhances CONGEST with limited global power in the form of the node-capacitated clique (NCC) model is considered, and the existence of a Laplacian solver with round complexity no(1) log(1/ε) is shown.

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