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arXiv · 2609.23852

A Simpler and Faster Min-Cost Flow Solver via Min-Ratio Cycles from Distance Oracles

Rasmus Kyng·Simon Meierhans·Maximilian Probst Gutenberg·Aurelio Sulser
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Abstract

The first almost-linear time maximum and minimum cost flow algorithm of Chen-Kyng-Liu-Peng-Probst Gutenberg-Sachdeva (FOCS 2022), reduced these flow objectives to a sequence of min-ratio cycle problems. Solving this core primitive requires approximately minimizing the ratio of a linear gradient term and an undirected length term. In Chen-Kyng-Liu-Peng-Probst Gutenberg-Sachdeva (FOCS 2022) and the subsequent work of Chen-Kyng-Liu-Meierhans-Probst Gutenberg (STOC 2024), intricate data structures were given to solve the min-ratio problem. We show that such a cycle can be extracted directly from the dynamic distance oracle of Kyng-Meierhans-Probst Gutenberg (STOC 2024) using linearity. This simplifies previous algorithms that relied on multiple additional steps to extract the cycle, and can be seen as evidence that solving the min-ratio cycle problem really is all about distances. As a result, we obtain a faster primal maxflow and min-cost flow solver that also extends to incremental graphs.

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Rasmus Kyng, Simon Meierhans, Maximilian Probst Gutenberg, Aurelio Sulser. 2026-09-20. A Simpler and Faster Min-Cost Flow Solver via Min-Ratio Cycles from Distance Oracles. https://arxiv.org/abs/2609.23852

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