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arXiv · 2510.27330

A Simple Deterministic Reduction From Gomory-Hu Tree to Maxflow and Expander Decomposition

Maximilian Probst Gutenberg·Weixuan Yuan
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Abstract

Given an undirected graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree on $V$ that preserves all-pairs mincuts of $G$ exactly. We present a simple and efficient randomized reduction from Gomory-Hu trees to polylog maxflow computations. On unweighted graphs, our reduction reduces to maxflow computations on graphs of total instance size $\tilde{O}(m)$ and the algorithm requires only $\tilde{O}(m)$ additional time. Our reduction is the first that is tight up to polylog factors. The reduction also seamlessly extends to weighted graphs, however, instance sizes and runtime increase to $\tilde{O}(n^2)$. Finally, we show how to extend our reduction to reduce Gomory-Hu trees for unweighted hypergraphs to maxflow in hypergraphs. Again, our reduction is the first that is tight up to polylog factors.

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Maximilian Probst Gutenberg, Weixuan Yuan. 2025-10-31. A Simple Deterministic Reduction From Gomory-Hu Tree to Maxflow and Expander Decomposition. https://arxiv.org/abs/2510.27330

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