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Betweenness Centrality – Incremental and Faster

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Book cover Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(v * · n) time, where v * is bounded by m *, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update problem. Even for a single edge update, our incremental algorithm is the first algorithm that is provably faster on sparse graphs than recomputing with the well-known static Brandes algorithm. It is also likely to be much faster than Brandes on dense graphs since m * is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(n · sort(v *)) cache misses, where sort is a well-known measure for caching efficiency.

This work was supported in part by NSF grants CCF-0830737 and CCF-1320675.

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Authors and Affiliations

  1. Indian Institute of Technology Madras, India

    Meghana Nasre

  2. University of Texas at Austin, USA

    Matteo Pontecorvi & Vijaya Ramachandran

Authors
  1. Meghana Nasre
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  2. Matteo Pontecorvi
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  3. Vijaya Ramachandran
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Nasre, M., Pontecorvi, M., Ramachandran, V. (2014). Betweenness Centrality – Incremental and Faster. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_49

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  • DOI: https://doi.org/10.1007/978-3-662-44465-8_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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