Faster Sparse Minimum Cost Flow by Electrical Flow Localization

@article{Axiotis2022FasterSM,
title={Faster Sparse Minimum Cost Flow by Electrical Flow Localization},
journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)},
year={2022},
pages={528-539}
}
• Published 19 November 2021
• Computer Science
• 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
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…
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