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A Distributed Multilevel Force-Directed Algorithm

  • Alessio Arleo
  • Walter Didimo
  • Giuseppe Liotta
  • Fabrizio Montecchiani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

The wide availability of powerful and inexpensive cloud computing services naturally motivates the study of distributed graph layout algorithms, able to scale to very large graphs. Nowadays, to process Big Data, companies are increasingly relying on PaaS infrastructures rather than buying and maintaining complex and expensive hardware. So far, only a few examples of basic force-directed algorithms that work in a distributed environment have been described. Instead, the design of a distributed multilevel force-directed algorithm is a much more challenging task, not yet addressed. We present the first multilevel force-directed algorithm based on a distributed vertex-centric paradigm, and its implementation on Giraph, a popular platform for distributed graph algorithms. Experiments show the effectiveness and the scalability of the approach. Using an inexpensive cloud computing service of Amazon, we draw graphs with ten million edges in about 60 min.

References

  1. 1.
  2. 2.
  3. 3.
  4. 4.
  5. 5.
    Arleo, A., Didimo, W., Liotta, G., Montecchiani, F.: A distributed force-directed algorithm on Giraph: design and experiments. ArXiv e-prints (2016). http://arxiv.org/abs/1606.02162
  6. 6.
    Arleo, A., Didimo, W., Liotta, G., Montecchiani, F.: A distributed multilevel force-directed algorithm. ArXiv e-prints (2016). http://arxiv.org/abs/1608.08522
  7. 7.
    Arleo, A., Didimo, W., Liotta, G., Montecchiani, F.: A million edge drawing for a fistful of dollars. In: Di Giacomo, E., Lubiw, A. (eds.) GD 2015. LNCS, vol. 9411, pp. 44–51. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-27261-0_4 CrossRefGoogle Scholar
  8. 8.
    Bartel, G., Gutwenger, C., Klein, K., Mutzel, P.: An experimental evaluation of multilevel layout methods. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 80–91. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-18469-7_8 CrossRefGoogle Scholar
  9. 9.
    Chae, S., Majumder, A., Gopi, M.: Hd-graphviz: Highly distributed graph visualization on tiled displays. In: ICVGIP 2012, pp. 43: 1–43: 8. ACM (2012)Google Scholar
  10. 10.
    Chimani, M., Gutwenger, C., Jünger, M., Klau, G.W., Klein, K., Mutzel, P.: The open graph drawing framework (OGDF). In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 543–569. CRC, Boca Raton (2013). http://www.ogdf.net/ Google Scholar
  11. 11.
    Ching, A.: Giraph: large-scale graph processing infrastructure on hadoop. In: Hadoop Summit (2011)Google Scholar
  12. 12.
    Ching, A., Edunov, S., Kabiljo, M., Logothetis, D., Muthukrishnan, S.: One trillion edges: graph processing at facebook-scale. PVLDB 8(12), 1804–1815 (2015)Google Scholar
  13. 13.
    Didimo, W., Montecchiani, F.: Fast layout computation of clustered networks: algorithmic advances and experimental analysis. Inf. Sci. 260, 185–199 (2014). http://dx.doi.org/10.1016/j.ins.2013.09.048 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  15. 15.
    Gajer, P., Goodrich, M.T., Kobourov, S.G.: A multi-dimensional approach to force-directed layouts of large graphs. Comput. Geom. 29(1), 3–18 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Godiyal, A., Hoberock, J., Garland, M., Hart, J.C.: Rapid multipole graph drawing on the GPU. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 90–101. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-00219-9_10 CrossRefGoogle Scholar
  17. 17.
    Hachul, S.: A potential field based multilevel algorithm for drawing large graphs. Ph.D. thesis, University of Cologne (2005). http://kups.ub.uni-koeln.de/volltexte/2005/1409/index.html
  18. 18.
    Hachul, S., Jünger, M.: Drawing large graphs with a potential-field-based multilevel algorithm. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 285–295. Springer, Heidelberg (2005). doi: 10.1007/978-3-540-31843-9_29 CrossRefGoogle Scholar
  19. 19.
    Hachul, S., Jünger, M.: Large-graph layout algorithms at work: an experimental study. J. Graph Algorithms Appl. 11(2), 345–369 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Hadany, R., Harel, D.: A multi-scale algorithm for drawing graphs nicely. Discrete Appl. Math. 113(1), 3–21 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Harel, D., Koren, Y.: A fast multi-scale method for drawing large graphs. J. Graph Algorithms Appl. 6(3), 179–202 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Hinge, A., Auber, D.: Distributed graph layout with Spark. In: IV 2015, pp. 271–276. IEEE (2015)Google Scholar
  23. 23.
    Hu, Y.: Efficient, high-quality force-directed graph drawing. Mathematica J. 10(1), 37–71 (2005)Google Scholar
  24. 24.
    Ingram, S., Munzner, T., Olano, M.: Glimmer: Multilevel MDS on the GPU. IEEE Trans. Vis. Comput. Graph. 15(2), 249–261 (2009)CrossRefGoogle Scholar
  25. 25.
    Kobourov, S.G.: Force-directed drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press, Boca Raton (2013)Google Scholar
  26. 26.
    Malewicz, G., Austern, M.H., Bik, A.J., Dehnert, J.C., Horn, I., Leiser, N., Czajkowski, G.: Pregel: A system for large-scale graph processing. In: SIGMOD 2010, pp. 135–146. ACM (2010)Google Scholar
  27. 27.
    Mueller, C., Gregor, D., Lumsdaine, A.: Distributed force-directed graph layout and visualization. In: EGPGV 2006, pp. 83–90. Eurographics (2006)Google Scholar
  28. 28.
    Rossi, R.A., Ahmed, N.K.: An interactive data repository with visual analytics. SIGKDD Explor. 17(2), 37–41 (2016). http://networkrepository.com CrossRefGoogle Scholar
  29. 29.
    Sharma, P., Khurana, U., Shneiderman, B., Scharrenbroich, M., Locke, J.: Speeding up network layout and centrality measures for social computing goals. In: Salerno, J., Yang, S.J., Nau, D., Chai, S.-K. (eds.) SBP 2011. LNCS, vol. 6589, pp. 244–251. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19656-0_35 CrossRefGoogle Scholar
  30. 30.
    Tikhonova, A., Ma, K.: A scalable parallel force-directed graph layout algorithm. In: EGPGV 2008, pp. 25–32. Eurographics (2008)Google Scholar
  31. 31.
    Valiant, L.G.: A bridging model for parallel computation. Commun. ACM 33(8), 103–111 (1990)CrossRefGoogle Scholar
  32. 32.
    Vaquero, L.M., Cuadrado, F., Logothetis, D., Martella, C.: Adaptive partitioning for large-scale dynamic graphs. In: ICDCS 2014, pp. 144–153. IEEE (2014)Google Scholar
  33. 33.
    Walshaw, C.: A multilevel algorithm for force-directed graph-drawing. J. Graph Algorithms Appl. 7(3), 253–285 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Yunis, E., Yokota, R., Ahmadia, A.: Scalable force directed graph layout algorithms using fast multipole methods. In: ISPDC 2012, pp. 180–187. IEEE (2012)Google Scholar
  35. 35.
    Zinsmaier, M., Brandes, U., Deussen, O., Strobelt, H.: Interactive level-of-detail rendering of large graphs. IEEE Trans. Vis. Comput. Graph. 18(12), 2486–2495 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Università Degli Studi di PerugiaPerugiaItaly

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