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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2021.21
URN: urn:nbn:de:0030-drops-146029
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14602/
Bläsius, Thomas ;
Friedrich, Tobias ;
Weyand, Christopher
Efficiently Computing Maximum Flows in Scale-Free Networks
Abstract
We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz’s algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz’s original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph.
Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.
BibTeX - Entry
@InProceedings{blasius_et_al:LIPIcs.ESA.2021.21,
author = {Bl\"{a}sius, Thomas and Friedrich, Tobias and Weyand, Christopher},
title = {{Efficiently Computing Maximum Flows in Scale-Free Networks}},
booktitle = {29th Annual European Symposium on Algorithms (ESA 2021)},
pages = {21:1--21:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-204-4},
ISSN = {1868-8969},
year = {2021},
volume = {204},
editor = {Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14602},
URN = {urn:nbn:de:0030-drops-146029},
doi = {10.4230/LIPIcs.ESA.2021.21},
annote = {Keywords: graphs, flow, network, scale-free}
}
