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Deterministic Minimum Steiner Cut in Maximum Flow Time

Authors Matthew Ding , Jason Li

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  • Theory of computation → Graph algorithms analysis
Keywords
  • graph algorithms
  • minimum cut
  • deterministic

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Abstract

We devise a deterministic algorithm for minimum Steiner cut, which uses (log n)^{O(1)} maximum flow calls and additional near-linear time. This algorithm improves on Li and Panigrahi’s (FOCS 2020) algorithm, which uses (log n)^{O(1/ε⁴)} maximum flow calls and additional O(m^{1+ε}) time, for ε > 0. Our algorithm thus shows that deterministic minimum Steiner cut can be solved in maximum flow time up to polylogarithmic factors, given any black-box deterministic maximum flow algorithm. Our main technical contribution is a novel deterministic graph decomposition method for terminal vertices that generalizes all existing s-strong partitioning methods, which we believe may have future applications.

Cite As Get BibTex

Matthew Ding and Jason Li. Deterministic Minimum Steiner Cut in Maximum Flow Time. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.46

Author Details

Matthew Ding
  • University of California, Berkeley, CA, USA
Jason Li
  • Carnegie Mellon University, Pittsburgh, PA, USA

Acknowledgements

Jason Li: This work was done while visiting the Simons Institute for the Theory of Computing. We want to thank Monika Henzinger, Satish Rao, and Di Wang for helpful discussions related to Lemma 11.

References

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  4. Matthew Ding and Jason Li. Deterministic minimum steiner cut in maximum flow time, 2023. URL: https://arxiv.org/abs/2312.16415.
  5. Monika Henzinger, Jason Li, Satish Rao, and Di Wang. Deterministic near-linear time minimum cut in weighted graphs. In 2024 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3089-3139, 2024. URL: https://doi.org/10.1137/1.9781611977912.111.
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