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arXiv:2611.08466 · v1

Canonical Cut Hierarchy in Almost-Linear Time via Reduction to Max-Flow

Karthekeyan ChandrasekaranHarshul Sagar
cs.DS
首次提交 2026-11-06 02:54
版本更新 2026-11-06 02:54
雷达观测 2026-11-06 12:09
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摘要

The canonical cut hierarchy recursively partitions a graph along Tutte-Nash-Williams partitions, choosing the partition with the most number of parts at each step. We give a randomized almost linear-time algorithm for computing this hierarchy in undirected graphs with polynomially bounded capacities via reduction to max-flow. This yields randomized almost linear-time algorithms for computing partition connectivity, strength, both arboricity and fractional arboricity, both integral and fractional spanning tree packing numbers, and implicit representations of the principal partition sequence and a maximum fractional spanning tree packing.

作者备注：39 pages, 5 figures

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作者提出一种随机化几乎线性时间算法，通过归约到最大流来计算无向图中的规范割层级，并由此得到多个图参数与结构的快速算法。

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v1 · 2026-11-06 02:54 · 最新观测版本

Canonical Cut Hierarchy in Almost-Linear Time via Reduction to Max-Flow

The canonical cut hierarchy recursively partitions a graph along Tutte-Nash-Williams partitions, choosing the partition with the most number of parts at each step. We give a randomized almost linear-time algorithm for computing this hierarchy in undirected graphs with polynomially bounded capacities via reduction to max-flow. This yields randomized almost linear-time algorithms for computing partition connectivity, strength, both arboricity and fractional arboricity, both integral and fractional spanning tree packing numbers, and implicit representations of the principal partition sequence and a maximum fractional spanning tree packing.

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