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Deterministic Maximum Flows in Simple Graphs

Author Tianyi Zhang

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Tianyi Zhang
  • Tsinghua University, Beijing, China

Acknowledgements

I want to thank helpful discussions with my advisor Ran Duan as well as my colleague Shucheng Chi.

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Tianyi Zhang. Deterministic Maximum Flows in Simple Graphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 114:1-114:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.114

Abstract

In this paper we are interested in deterministically computing maximum flows in undirected simple graphs where edges have unit capacities. When the input graph has n vertices and m edges, and the maximum flow is known to be upper bounded by τ as prior knowledge, our algorithm has running time Õ(m + n^{5/3}τ^{1/2}); in the extreme case where τ = Θ(n), our algorithm has running time Õ(n^{2.17}). This always improves upon the previous best deterministic upper bound Õ(n^{9/4}τ^{1/8}) by [Duan, 2013]. Furthermore, when τ ≥ n^{0.67} our algorithm is faster than a classical upper bound of O(m + nτ^{3/2}) by [Karger and Levin, 1998].

Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
Keywords
  • graph algorithms
  • maximum flows
  • dynamic data structures

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References

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