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2016 | OriginalPaper | Buchkapitel

A Distributed Multilevel Force-Directed Algorithm

verfasst von : Alessio Arleo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani

Erschienen in: Graph Drawing and Network Visualization

Verlag: Springer International Publishing

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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.

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Literatur
7.
Zurück zum Zitat 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 CrossRef 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 CrossRef
8.
Zurück zum Zitat 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 CrossRef 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 CrossRef
9.
Zurück zum Zitat 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) 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)
10.
Zurück zum Zitat 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/ 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/​
11.
Zurück zum Zitat Ching, A.: Giraph: large-scale graph processing infrastructure on hadoop. In: Hadoop Summit (2011) Ching, A.: Giraph: large-scale graph processing infrastructure on hadoop. In: Hadoop Summit (2011)
12.
Zurück zum Zitat Ching, A., Edunov, S., Kabiljo, M., Logothetis, D., Muthukrishnan, S.: One trillion edges: graph processing at facebook-scale. PVLDB 8(12), 1804–1815 (2015) Ching, A., Edunov, S., Kabiljo, M., Logothetis, D., Muthukrishnan, S.: One trillion edges: graph processing at facebook-scale. PVLDB 8(12), 1804–1815 (2015)
14.
Zurück zum Zitat Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)CrossRef Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)CrossRef
15.
Zurück zum Zitat 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
16.
Zurück zum Zitat 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 CrossRef 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 CrossRef
18.
19.
Zurück zum Zitat Hachul, S., Jünger, M.: Large-graph layout algorithms at work: an experimental study. J. Graph Algorithms Appl. 11(2), 345–369 (2007)MathSciNetCrossRefMATH Hachul, S., Jünger, M.: Large-graph layout algorithms at work: an experimental study. J. Graph Algorithms Appl. 11(2), 345–369 (2007)MathSciNetCrossRefMATH
20.
21.
22.
Zurück zum Zitat Hinge, A., Auber, D.: Distributed graph layout with Spark. In: IV 2015, pp. 271–276. IEEE (2015) Hinge, A., Auber, D.: Distributed graph layout with Spark. In: IV 2015, pp. 271–276. IEEE (2015)
23.
Zurück zum Zitat Hu, Y.: Efficient, high-quality force-directed graph drawing. Mathematica J. 10(1), 37–71 (2005) Hu, Y.: Efficient, high-quality force-directed graph drawing. Mathematica J. 10(1), 37–71 (2005)
24.
Zurück zum Zitat Ingram, S., Munzner, T., Olano, M.: Glimmer: Multilevel MDS on the GPU. IEEE Trans. Vis. Comput. Graph. 15(2), 249–261 (2009)CrossRef Ingram, S., Munzner, T., Olano, M.: Glimmer: Multilevel MDS on the GPU. IEEE Trans. Vis. Comput. Graph. 15(2), 249–261 (2009)CrossRef
25.
Zurück zum Zitat Kobourov, S.G.: Force-directed drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press, Boca Raton (2013) Kobourov, S.G.: Force-directed drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press, Boca Raton (2013)
26.
Zurück zum Zitat 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) 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)
27.
Zurück zum Zitat Mueller, C., Gregor, D., Lumsdaine, A.: Distributed force-directed graph layout and visualization. In: EGPGV 2006, pp. 83–90. Eurographics (2006) Mueller, C., Gregor, D., Lumsdaine, A.: Distributed force-directed graph layout and visualization. In: EGPGV 2006, pp. 83–90. Eurographics (2006)
29.
Zurück zum Zitat 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 CrossRef 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 CrossRef
30.
Zurück zum Zitat Tikhonova, A., Ma, K.: A scalable parallel force-directed graph layout algorithm. In: EGPGV 2008, pp. 25–32. Eurographics (2008) Tikhonova, A., Ma, K.: A scalable parallel force-directed graph layout algorithm. In: EGPGV 2008, pp. 25–32. Eurographics (2008)
31.
Zurück zum Zitat Valiant, L.G.: A bridging model for parallel computation. Commun. ACM 33(8), 103–111 (1990)CrossRef Valiant, L.G.: A bridging model for parallel computation. Commun. ACM 33(8), 103–111 (1990)CrossRef
32.
Zurück zum Zitat Vaquero, L.M., Cuadrado, F., Logothetis, D., Martella, C.: Adaptive partitioning for large-scale dynamic graphs. In: ICDCS 2014, pp. 144–153. IEEE (2014) Vaquero, L.M., Cuadrado, F., Logothetis, D., Martella, C.: Adaptive partitioning for large-scale dynamic graphs. In: ICDCS 2014, pp. 144–153. IEEE (2014)
33.
34.
Zurück zum Zitat Yunis, E., Yokota, R., Ahmadia, A.: Scalable force directed graph layout algorithms using fast multipole methods. In: ISPDC 2012, pp. 180–187. IEEE (2012) Yunis, E., Yokota, R., Ahmadia, A.: Scalable force directed graph layout algorithms using fast multipole methods. In: ISPDC 2012, pp. 180–187. IEEE (2012)
35.
Zurück zum Zitat 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)CrossRef 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)CrossRef
Metadaten
Titel
A Distributed Multilevel Force-Directed Algorithm
verfasst von
Alessio Arleo
Walter Didimo
Giuseppe Liotta
Fabrizio Montecchiani
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-50106-2_1