Estimating Clustering Indexes in Data Streams

L.S. Buriol, G. Frahling, S. Leonardi, C. Sohler, in: Proceedings of the 15th European Symposium on Algorithms (ESA), Springer, Berlin, Heidelberg, 2007, pp. 618–632.

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Abstract
We present random sampling algorithms that with probability at least 1 − δ compute a (1 ±ε)-approximation of the clustering coefficient and of the number of bipartite clique subgraphs of a graph given as an incidence stream of edges. The space used by our algorithm to estimate the clustering coefficient is inversely related to the clustering coefficient of the network itself. The space used by our algorithm to compute the number K 3,3 of bipartite cliques is proportional to the ratio between the number of K 1,3 and K 3,3 in the graph. Since the space complexity depends only on the structure of the input graph and not on the number of nodes, our algorithms scale very well with increasing graph size. Therefore they provide a basic tool to analyze the structure of dense clusters in large graphs and have many applications in the discovery of web communities, the analysis of the structure of large social networks and the probing of frequent patterns in large graphs. We implemented both algorithms and evaluated their performance on networks from different application domains and of different size; The largest instance is a webgraph consisting of more than 135 million nodes and 1 billion edges. Both algorithms compute accurate results in reasonable time on the tested instances.
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Proceedings Title
Proceedings of the 15th European Symposium on Algorithms (ESA)
Volume
4698
Page
618-632
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Buriol LS, Frahling G, Leonardi S, Sohler C. Estimating Clustering Indexes in Data Streams. In: Proceedings of the 15th European Symposium on Algorithms (ESA). Vol 4698. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer; 2007:618-632. doi:10.1007/978-3-540-75520-3_55
Buriol, L. S., Frahling, G., Leonardi, S., & Sohler, C. (2007). Estimating Clustering Indexes in Data Streams. In Proceedings of the 15th European Symposium on Algorithms (ESA) (Vol. 4698, pp. 618–632). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-540-75520-3_55
@inproceedings{Buriol_Frahling_Leonardi_Sohler_2007, place={Berlin, Heidelberg}, series={Lecture Notes in Computer Science}, title={Estimating Clustering Indexes in Data Streams}, volume={4698}, DOI={10.1007/978-3-540-75520-3_55}, booktitle={Proceedings of the 15th European Symposium on Algorithms (ESA)}, publisher={Springer}, author={Buriol, Luciana S. and Frahling, Gereon and Leonardi, Stefano and Sohler, Christian}, year={2007}, pages={618–632}, collection={Lecture Notes in Computer Science} }
Buriol, Luciana S., Gereon Frahling, Stefano Leonardi, and Christian Sohler. “Estimating Clustering Indexes in Data Streams.” In Proceedings of the 15th European Symposium on Algorithms (ESA), 4698:618–32. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, 2007. https://doi.org/10.1007/978-3-540-75520-3_55.
L. S. Buriol, G. Frahling, S. Leonardi, and C. Sohler, “Estimating Clustering Indexes in Data Streams,” in Proceedings of the 15th European Symposium on Algorithms (ESA), 2007, vol. 4698, pp. 618–632.
Buriol, Luciana S., et al. “Estimating Clustering Indexes in Data Streams.” Proceedings of the 15th European Symposium on Algorithms (ESA), vol. 4698, Springer, 2007, pp. 618–32, doi:10.1007/978-3-540-75520-3_55.

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