License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.69
URN: urn:nbn:de:0030-drops-181212
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18121/
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Goranci, Gramoz ; Henzinger, Monika

Efficient Data Structures for Incremental Exact and Approximate Maximum Flow

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LIPIcs-ICALP-2023-69.pdf (0.8 MB)

Abstract

We show an (1+ε)-approximation algorithm for maintaining maximum s-t flow under m edge insertions in m^{1/2+o(1)} ε^{-1/2} amortized update time for directed, unweighted graphs. This constitutes the first sublinear dynamic maximum flow algorithm in general sparse graphs with arbitrarily good approximation guarantee.
Furthermore we give an algorithm that maintains an exact maximum s-t flow under m edge insertions in an n-node graph in Õ(n^{5/2}) total update time. For sufficiently dense graphs, this gives to the first exact incremental algorithm with sub-linear amortized update time for maintaining maximum flows.

BibTeX - Entry

@InProceedings{goranci_et_al:LIPIcs.ICALP.2023.69,
  author =	{Goranci, Gramoz and Henzinger, Monika},
  title =	{{Efficient Data Structures for Incremental Exact and Approximate Maximum Flow}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18121},
  URN =		{urn:nbn:de:0030-drops-181212},
  doi =		{10.4230/LIPIcs.ICALP.2023.69},
  annote =	{Keywords: dynamic graph algorithms, maximum flow, data structures}
}

Keywords: dynamic graph algorithms, maximum flow, data structures
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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