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DOI: 10.4230/LIPIcs.ISAAC.2018.36
URN: urn:nbn:de:0030-drops-99846
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9984/
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Bentert, Matthias ; Dittmann, Alexander ; Kellerhals, Leon ; Nichterlein, André ; Niedermeier, Rolf

An Adaptive Version of Brandes' Algorithm for Betweenness Centrality

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Abstract

Betweenness centrality - measuring how many shortest paths pass through a vertex - is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [2001] computes, on an n-vertex and m-edge graph, the betweenness centrality of all vertices in O(nm) worst-case time. In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices. Based on these three algorithmic ingredients, we provide a strengthened worst-case running time analysis for betweenness centrality algorithms. More specifically, we prove an adaptive running time bound O(kn), where k < m is the size of a minimum feedback edge set of the input graph.

BibTeX - Entry

@InProceedings{bentert_et_al:LIPIcs:2018:9984,
  author =	{Matthias Bentert and Alexander Dittmann and Leon Kellerhals and Andr{\'e} Nichterlein and Rolf Niedermeier},
  title =	{{An Adaptive Version of Brandes' Algorithm for Betweenness Centrality}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9984},
  URN =		{urn:nbn:de:0030-drops-99846},
  doi =		{10.4230/LIPIcs.ISAAC.2018.36},
  annote =	{Keywords: network science, social network analysis, centrality measures, shortest paths, tree-like graphs, efficient pre- and postprocessing, FPT in P}
}

Keywords: network science, social network analysis, centrality measures, shortest paths, tree-like graphs, efficient pre- and postprocessing, FPT in P
Seminar: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 27.11.2018


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