Efficient triangle counting in large graphs via degree-based vertex partitioning

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6516 LNCS, Issue , 2010, Pages 15-24

  Kolountzakis, Mihail N ^a   Miller, Gary L ^b   Peng, Richard ^b   Tsourakakis, Charalampos E ^c  

^a UNIVERSITY OF CRETE   (Greece)

^b Carnegie Mellon University   (United States)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LARGE GRAPHS; LOW DEGREE; MULTIPLICATIVE ERRORS; NUMBER OF TRIANGLES; RANDOM PROJECTIONS; RUNNING TIME; SAMPLING ALGORITHM; SPACE USAGE; SUFFICIENT CONDITIONS;

ALGORITHMS; DRUG PRODUCTS PLANTS; COMPUTER SCIENCE; COMPUTERS;

MATHEMATICAL MODELS; ARTIFICIAL INTELLIGENCE;

EID: 78650884385     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-18009-5_3     Document Type: Conference Paper

References (35)

1. Alon, N., Yuster, R., Zwick, U.: Finding and Counting Given Length Cycles. Algorithmica 17(3), 209-223 (1997) (Pubitemid 127440916)
2. Avron, H.: Counting triangles in large graphs using randomized matrix trace estimation. In: Proceedings of KDD-LDMTA 2010 (2010)
3. Bar-Yosseff, Z., Kumar, R., Sivakumar, D.: Reductions in streaming algorithms, with an application to counting triangles in graphs. In: SODA (2002)
4. Becchetti, L., Boldi, P., Castillo, C., Gionis, A.: Efficient Semi-Streaming Algorithms for Local Triangle Counting in Massive Graphs. In: KDD (2008)
5. Buriol, L., Frahling, G., Leonardi, S., Marchetti-Spaccamela, A., Sohler, C.: Counting Triangles in Data Streams. In: PODS (2006)
6. Chernoff, H.: A Note on an Inequality Involving the Normal Distribution. Annals of Probability 9(3), 533-535 (1981)
7. Chung, F., Lu, L.: Complex Graphs and Networks, vol. (107). American Mathematical Society, Providence (2006)
8. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. In: STOC (1987)
9. Jeffrey, D., Ghemawat, S.: MapReduce: Simplified Data Processing on Large Clusters. In: OSDI (2004)
10. Eckmann, J.-P., Moses, E.: Curvature of co-links uncovers hidden thematic layers in the World Wide Web. In: PNAS (2002)
11. Frank, O., Strauss, D.: Markov Graphs. Journal of the American Statistical Association 81(395), 832-842 (1986)
12. Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: On graph problems in a semi-streaming model. Journal of Theoretical Computer Science 348(2), 207-216 (2005)
13. Hajnal, A., Szemerédi, E.: Proof of a Conjecture of Erds. In: Combinatorial Theory and Its Applications, vol. 2, pp. 601-623. North-Holland, Amsterdam (1970)
14. Itai, A., Rodeh, M.: Finding a minimum circuit in a graph. In: STOC (1977)
15. Johnson, W., Lindenstrauss, J.: Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics 26, 189-206 (1984)
16. Jowhari, H., Ghodsi, M.: New Streaming Algorithms for Counting Triangles in Graphs. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 710-716. Springer, Heidelberg (2005)
17. Kang, U., Tsourakakis, C., Appel, A.P., Faloutsos, C., Leskovec, J.: Radius Plots for Mining Tera-byte Scale Graphs: Algorithms, Patterns, and Observations. In: SIAM Data Mining, SDM 2010 (2010)
18. Kang, U., Tsourakakis, C., Faloutsos, C.: PEGASUS: A Peta-Scale Graph Mining System. In: IEEE Data Mining, ICDM 2009 (2009)
19. Kim, J.H., Vu, V.H.: Concentration of multivariate polynomials and its applications. Combinatorica 20(3), 417-434 (2000)
20. Knuth, D.: Seminumerical Algorithms, 3rd edn. Addison-Wesley Professional, Reading (1997)
21. Kolountzakis, M., Miller, G.L., Peng, R., Tsourakakis, C.E.: Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning, http://arxiv.org/abs/1011.0468
22. Latapy, M.: Main-memory triangle computations for very large (sparse (power-law)) graphs. Theor. Comput. Sci. 407, 458-473 (2008)
23. Magen, A., Zouzias, A.: Near Optimal Dimensionality Reductions That Preserve Volumes. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 523-534. Springer, Heidelberg (2008)
24. Mislove, A., Massimiliano, M., Gummadi, K., Druschel, P., Bhattacharjee, B.: Measurement and Analysis of Online Social Networks. In: IMC (2007)
25. Newman, M.: The structure and function of complex networks (2003)
26. Papadimitriou, C., Yannakakis, M.: The clique problem for planar graphs. Information Processing Letters 13, 131-133 (1981)
27. Schank, T., Wagner, D.: Finding, Counting and Listing all Triangles in Large Graphs, An Experimental Study. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 606-609. Springer, Heidelberg (2005)
28. Schank, T., Wagner, D.: Approximating Clustering Coefficient and Transitivity. Journal of Graph Algorithms and Applications 9, 265-275 (2005)
29. Tsourakakis, C.E.: Fast Counting of Triangles in Large Real Networks, without counting: Algorithms and Laws. In: ICDM (2008)
30. Tsourakakis, C.E.: Counting Triangles Using Projections. KAIS Journal (2010)
31. Tsourakakis, C.E., Kang, U., Miller, G.L., Faloutsos, C.: Doulion: Counting Triangles in Massive Graphs with a Coin. In: KDD (2009)
32. Tsourakakis, C.E., Kolountzakis, M., Miller, G.L.: Approximate Triangle Counting (Preprint), http://arxiv.org/abs/0904.3761
33. Tsourakakis, C.E., Drineas, P., Michelakis, E., Koutis, I., Faloutsos, C.: Spectral Counting of Triangles via Element-Wise Sparsification and Triangle-Based Link Recommendation. In: ASONAM (2010)
34. Vu, V.H.: On the concentration of multivariate polynomials with small expectation. Random Structures and Algorithms 16(4), 344-363 (2000)
35. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications (Structural Analysis in the Social Sciences). Cambridge University Press, Cambridge (1994)