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arXiv · 2511.10036

Faster All-Pairs Minimum Cut: Bypassing Exact Max-Flow

Yotam Kenneth-Mordoch·Robert Krauthgamer
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Abstract

All-Pairs Minimum Cut (APMC) is a fundamental graph problem that asks to find a minimum $s,t$-cut for every pair of vertices $s,t$. A recent line of work on fast algorithms for APMC has culminated with a reduction of APMC to $\mathrm{polylog}(n)$-many max-flow computations. But unfortunately, no fast algorithms are currently known for exact max-flow in several standard models of computation, such as the cut-query model and the fully-dynamic model. Our main technical contribution is a sparsifier that preserves all minimum $s,t$-cuts in an unweighted graph, and can be constructed using only approximate max-flow computations. We then use this sparsifier to devise new algorithms for APMC in unweighted graphs in several computational models: (i) a randomized algorithm that makes $\tilde{O}(n^{3/2})$ cut queries to the input graph; (ii) a deterministic fully-dynamic algorithm with $n^{3/2+o(1)}$ worst-case update time; and (iii) a randomized two-pass streaming algorithm with space requirement $\tilde{O}(n^{3/2})$. These results improve over the known bounds, even for (single pair) minimum $s,t$-cut in the respective models.

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BibTeXRIS

Yotam Kenneth-Mordoch, Robert Krauthgamer. 2026-04-06. Faster All-Pairs Minimum Cut: Bypassing Exact Max-Flow. https://arxiv.org/abs/2511.10036

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