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arXiv · 2608.17384

Maximum Flow Without the Outer IPM

Jason Li·Alex Wice
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Abstract

We show that the balancing weights technique of Li (2026) actually produces an approximate *pseudo-circulation* of a directed, capacitated graph in $m^{1+o(1)}$ time. Together with standard flow techniques, we obtain an $m^{1+o(1)}$ time maximum flow algorithm that avoids the interior-point method framework of recent almost-linear time algorithms (Chen et al. FOCS 2022, van den Brand et al. FOCS 2024).

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Jason Li, Alex Wice. 2026-08-18. Maximum Flow Without the Outer IPM. https://arxiv.org/abs/2608.17384

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