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arXiv:2611.10181 · v1

A Note on the Hardness of Partially Dynamic Max Flow

Thatchaphol SaranurakBenyu Wang
cs.DS
首次提交 2026-11-07 04:02
版本更新 2026-11-07 04:02
雷达观测 2026-11-10 10:11
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摘要

We study the fine-grained complexity of partially dynamic max flow in capacitated graphs. Assuming the combinatorial 4-clique hypothesis, combinatorial algorithms require $Ω(n^{2-o(1)})$ amortized update time. Thus, recomputing max flow after each update is optimal up to subpolynomial factors for combinatorial algorithms in dense graphs. The previous conditional lower bound was $Ω(n^{1-o(1)})$ amortized update time under SETH or the OMv hypothesis and applies to all algorithms [Dah16].

作者备注：SOSA 2027

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v1 · 2026-11-07 04:02 · 最新观测版本

A Note on the Hardness of Partially Dynamic Max Flow

We study the fine-grained complexity of partially dynamic max flow in capacitated graphs. Assuming the combinatorial 4-clique hypothesis, combinatorial algorithms require $Ω(n^{2-o(1)})$ amortized update time. Thus, recomputing max flow after each update is optimal up to subpolynomial factors for combinatorial algorithms in dense graphs. The previous conditional lower bound was $Ω(n^{1-o(1)})$ amortized update time under SETH or the OMv hypothesis and applies to all algorithms [Dah16].

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