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KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

Authors Michele Borassi, Emanuele Natale

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Michele Borassi
Emanuele Natale

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Michele Borassi and Emanuele Natale. KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ESA.2016.20

Abstract

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks.
The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest.

The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time |E|^{1/2+o(1)} with high probability, obtaining a significant speedup with respect to the Theta(|E|) worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well.

The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the k most central nodes. Furthermore, our analysis is general, and it might be extended to other settings, as well.

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Keywords
  • Betweenness centrality
  • shortest path algorithm
  • graph mining
  • sampling
  • network analysis

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