LIPIcs.ESA.2024.46.pdf
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Deterministic Minimum Steiner Cut in Maximum Flow Time
Authors
Matthew Ding 
,
Jason Li
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Volume:
32nd Annual European Symposium on Algorithms (ESA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-23
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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.
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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
https://doi.org/10.4230/LIPIcs.ESA.2024.46
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Graph algorithms analysis
Keywords
- graph algorithms
- minimum cut
- deterministic
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References
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