Fully-Dynamic Approximation of Betweenness Centrality

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)

Abstract

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions.

In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of this upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions.

Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude.

Keywords

betweenness centrality algorithmic network analysis fully-dynamic graph algorithms approximation algorithms shortest paths 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bader, D.A., Kintali, S., Madduri, K., Mihail, M.: Approximating betweenness centrality. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 124–137. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Bauer, R., Wagner, D.: Batch dynamic single-source shortest-path algorithms: An experimental study. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 51–62. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Bergamini, E., Meyerhenke, H.: Fully-dynamic approximation of betweenness centrality. CoRR, abs/1504.07091 (2015)Google Scholar
  4. 4.
    Bergamini, E., Meyerhenke, H., Staudt, C.: Approximating betweenness centrality in large evolving networks. In: 17th Workshop on Algorithm Engineering and Experiments, ALENEX 2015, pp. 133–146. SIAM (2015)Google Scholar
  5. 5.
    Brandes, U.: A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163–177 (2001)CrossRefMATHGoogle Scholar
  6. 6.
    Brandes, U., Pich, C.: Centrality estimation in large networks. I. J. Bifurcation and Chaos 17(7), 2303–2318 (2007)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    D’Andrea, A., D’Emidio, M., Frigioni, D., Leucci, S., Proietti, G.: Experimental evaluation of dynamic shortest path tree algorithms on homogeneous batches. In: Gudmundsson, J., Katajainen, J. (eds.) SEA 2014. LNCS, vol. 8504, pp. 283–294. Springer, Heidelberg (2014)Google Scholar
  8. 8.
    Frigioni, D., Marchetti-Spaccamela, A., Nanni, U.: Semi-dynamic algorithms for maintaining single-source shortest path trees. Algorithmica 22, 250–274 (2008)CrossRefMATHGoogle Scholar
  9. 9.
    Geisberger, R., Sanders, P., Schultes, D.: Better approximation of betweenness centrality. In: 10th Workshop on Algorithm Engineering and Experiments, ALENEX 2008, pp. 90–100. SIAM (2008)Google Scholar
  10. 10.
    Goel, K., Singh, R.R., Iyengar, S., Sukrit: A faster algorithm to update betweenness centrality after node alteration. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds.) WAW 2013. LNCS, vol. 8305, pp. 170–184. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Green, O., McColl, R., Bader, D.A.: A fast algorithm for streaming betweenness centrality. In: SocialCom/PASSAT, pp. 11–20. IEEE (2012)Google Scholar
  12. 12.
    Kas, M., Carley, K.M., Carley, L.R.: An incremental algorithm for updating betweenness centrality and k-betweenness centrality and its performance on realistic dynamic social network data. Social Netw. Analys. Mining 4(1), 235 (2014)CrossRefGoogle Scholar
  13. 13.
    Kourtellis, N., De Francisci Morales, G., Bonchi, F.: Scalable online betweenness centrality in evolving graphs. IEEE Transactions on Knowledge and Data Engineering (99), 1 (2015)Google Scholar
  14. 14.
    Kunegis, J.: KONECT: the koblenz network collection. In: 22nd Int. World Wide Web Conf., WWW 2013, pp. 1343–1350 (2013)Google Scholar
  15. 15.
    Lee, M., Lee, J., Park, J.Y., Choi, R.H., Chung, C.: QUBE: a quick algorithm for updating betweenness centrality. In: 21st World Wide Web Conf. 2012, WWW 2012, pp. 351–360. ACM (2012)Google Scholar
  16. 16.
    Leskovec, J., Kleinberg, J.M., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: 11th Int. Conf. on Knowledge Discovery and Data Mining, pp. 177–187. ACM (2005)Google Scholar
  17. 17.
    Nasre, M., Pontecorvi, M., Ramachandran, V.: Betweenness centrality – incremental and faster. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014, Part II. LNCS, vol. 8635, pp. 577–588. Springer, Heidelberg (2014)Google Scholar
  18. 18.
    Ramalingam, G., Reps, T.: An incremental algorithm for a generalization of the shortest-path problem. Journal of Algorithms 21, 267–305 (1992)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Riondato, M., Kornaropoulos, E.M.: Fast approximation of betweenness centrality through sampling. In: 7th ACM Int. Conf. on Web Search and Data Mining (WSDM 2014), pp. 413–422. ACM (2014)Google Scholar
  20. 20.
    Roditty, L., Zwick, U.: On dynamic shortest paths problems. Algorithmica 61(2), 389–401 (2011)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    von Looz, M., Staudt, C.L., Meyerhenke, H., Prutkin, R.: Fast generation of complex networks with underlying hyperbolic geometry (2015), http://arxiv.org/abs/1501.03545v2
  22. 22.
    Staudt, C., Sazonovs, A., Meyerhenke, H.: NetworKit: An interactive tool suite for high-performance network analysis (2014), http://arxiv.org/abs/1403.3005

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations