Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Enoch, Julian; Fox, Kyle; Mesica, Dor; Mozes, Shay https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-155057
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A Faster Algorithm for Maximum Flow in Directed Planar Graphs with Vertex Capacities

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Abstract

We give an O(k³ Δ n log n min(k, log² n) log²(nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks. This improves by a factor of max(k²,k log² n) over the fastest algorithm previously known for this problem [Wang, SODA 2019].
The speedup is obtained by two independent ideas. First we replace an iterative procedure of Wang that uses O(k) invocations of an O(k³ n log³ n)-time algorithm for maximum flow algorithm in a planar graph with k apices [Borradaile et al., FOCS 2012, SICOMP 2017], by an alternative procedure that only makes one invocation of the algorithm of Borradaile et al. Second, we show two alternatives for computing flows in the k-apex graphs that arise in our modification of Wang’s procedure faster than the algorithm of Borradaile et al. In doing so, we introduce and analyze a sequential implementation of the parallel highest-distance push-relabel algorithm of Goldberg and Tarjan [JACM 1988].

BibTeX - Entry

@InProceedings{enoch_et_al:LIPIcs.ISAAC.2021.72,
  author =	{Enoch, Julian and Fox, Kyle and Mesica, Dor and Mozes, Shay},
  title =	{{A Faster Algorithm for Maximum Flow in Directed Planar Graphs with Vertex Capacities}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15505},
  URN =		{urn:nbn:de:0030-drops-155057},
  doi =		{10.4230/LIPIcs.ISAAC.2021.72},
  annote =	{Keywords: flow, planar graphs, vertex capacities}
}

Keywords: flow, planar graphs, vertex capacities
Seminar: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue date: 2021
Date of publication: 30.11.2021


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