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arXiv · 2510.16741

All-Pairs Minimum Cut using $\tilde{O}(n^{7/4})$ Cut Queries

Yotam Kenneth-Mordoch·Robert Krauthgamer
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Abstract

We present the first non-trivial algorithm for the all-pairs minimum cut problem in the cut-query model. Given cut-query access to an unweighted graph $G=(V,E)$ with $n$ vertices, our randomized algorithm constructs a Gomory-Hu tree of $G$, and thus solves the all-pairs minimum cut problem, using $\tilde{O}(n^{7/4})$ cut queries.

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Yotam Kenneth-Mordoch, Robert Krauthgamer. 2025-10-19. All-Pairs Minimum Cut using $\tilde{O}(n^{7/4})$ Cut Queries. https://arxiv.org/abs/2510.16741

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