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URN: urn:nbn:de:0030-drops-141832
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Deterministic Maximum Flows in Simple Graphs

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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].

BibTeX - Entry

@InProceedings{zhang:LIPIcs.ICALP.2021.114,
  author =	{Zhang, Tianyi},
  title =	{{Deterministic Maximum Flows in Simple Graphs}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{114:1--114:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14183},
  URN =		{urn:nbn:de:0030-drops-141832},
  doi =		{10.4230/LIPIcs.ICALP.2021.114},
  annote =	{Keywords: graph algorithms, maximum flows, dynamic data structures}
}

Keywords: graph algorithms, maximum flows, dynamic data structures
Seminar: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue date: 2021
Date of publication: 02.07.2021


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