Abstract
In this paper we propose a new algorithm for computing the diameter of directed unweighted graphs. Even though, in the worst case, this algorithm has complexity O(nm), where n is the number of nodes and m is the number of edges of the graph, we experimentally show that in practice our method works in O(m) time. Moreover, we show how to extend our algorithm to the case of directed weighted graphs and, even in this case, we present some preliminary very positive experimental results.
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References
Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four Degrees of Separation (2011) arXiv:1111.4570v1
Bansal, S., Khandelwal, S., Meyers, L.: Exploring biological network structure with clustered random networks. BMC Bioinformatics 10(1), 405+ (2009)
Boldi, P., Vigna, S.: The WebGraph Framework I: Compression Techniques. In: Proceedings of the 13th International World Wide Web Conference, pp. 595–601. ACM Press, Manhattan (2003)
Boldi, P., Rosa, M., Vigna, S.: Hyperanf: approximating the neighbourhood function of very large graphs on a budget. In: WWW, pp. 625–634 (2011)
Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. Springer (2005)
Broder, A.Z., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.L.: Graph structure in the web. Computer Networks 33(1-6), 309–320 (2000)
9th DIMACS Implementation Challenge - Shortest Paths (2006), http://www.dis.uniroma1.it/~challenge9/
Chepoi, V., Dragan, F., Estellon, B., Habib, M., Vaxès, Y.: Diameters, centers, and approximating trees of delta-hyperbolic geodesic spaces and graphs. In: Proceedings of the 24th Annual Symposium on Computational Geometry, SCG 2008, pp. 59–68. ACM, New York (2008)
Crescenzi, P., Grossi, R., Habib, M., Lanzi, L., Marino, A.: On Computing the Diameter of Real-World Undirected Graphs. Presented at Workshop on Graph Algorithms and Applications (Zurich–July 3, 2011) and selected for submission to the special issue of Theoretical Computer Science in honor of Giorgio Ausiello in the occasion of his 70th birthday (2011)
Crescenzi, P., Grossi, R., Imbrenda, C., Lanzi, L., Marino, A.: Finding the Diameter in Real-World Graphs. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part I. LNCS, vol. 6346, pp. 302–313. Springer, Heidelberg (2010)
Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Havlin, S., Cohen, R.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)
Junker, B.O.H., Schreiber, F.: Analysis of Biological Networks. Wiley Series in Bioinformatics. Wiley Interscience (2008)
Kang, U., Tsourakakis, C.E., Appel, A.P., Faloutsos, C., Leskovec, J.: Hadi: Mining radii of large graphs. TKDD 5(2), 8 (2011)
Kang, U., Tsourakakis, C.E., Faloutsos, C.: PEGASUS: A Peta-Scale graph mining system implementation and observations. In: 2009 Ninth IEEE International Conference on Data Mining, pp. 229–238. IEEE (December 2009)
Latapy, M., Magnien, C.: Measuring Fundamental Properties of Real-World Complex Networks. CoRR abs/cs/0609115 (2006)
Leskovec, J., Faloutsos, C.: Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2006, pp. 631–636. ACM, New York (2006)
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics 6(1), 29–123 (2009)
Mehlhorn, K., Meyer, U.: External-Memory Breadth-First Search with Sublinear I/O. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 723–735. Springer, Heidelberg (2002)
Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, IMC 2007, pp. 29–42. ACM, New York (2007)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
Palmer, C.R., Gibbons, P.B., Faloutsos, C.: ANF: a Fast and Scalable Tool for Data Mining in Massive Graphs. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 81–90 (2002)
SNAP: Stanford Network Analysis Package (SNAP) (2009), http://snap.stanford.edu
Takes, F.W., Kosters, W.A.: Determining the diameter of small world networks. In: CIKM, pp. 1191–1196 (2011)
Network datasets (2009), http://toreopsahl.com/datasets/
Wang, F., Moreno, Y., Sun, Y.: Structure of peer-to-peer social networks. Phys. Rev. E 73, 036123 (2006)
WebGraph: WebGraph (2001), http://webgraph.dsi.unimi.it/
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Crescenzi, P., Grossi, R., Lanzi, L., Marino, A. (2012). On Computing the Diameter of Real-World Directed (Weighted) Graphs. In: Klasing, R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30850-5_10
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DOI: https://doi.org/10.1007/978-3-642-30850-5_10
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