Advertisement

Incremental Algorithms for Sampling Dynamic Graphs

  • Xuesong Lu
  • Tuan Quang Phan
  • Stéphane Bressan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8055)

Abstract

Among the many reasons that justify the need for efficient and effective graph sampling algorithms is the ability to replace a graph too large to be processed by a tractable yet representative subgraph. For instance, some approximation algorithms start by looking for a solution on a sample subgraph and then extrapolate it. The sample graph should be of manageable size. The sample graph should preserve properties of interest. There exist several efficient and effective algorithms for the sampling of graphs. However, the graphs encountered in modern applications are dynamic: edges and vertices are added or removed. Existing graph sampling algorithms are not incremental. They were designed for static graphs. If the original graph changes, the sample must be entirely recomputed. Is it possible to design an algorithm that reuses whole or part of the already computed sample?

We present two incremental graph sampling algorithms preserving selected properties. The rationale of the algorithms is to replace a fraction of vertices in the former sample with newly updated vertices. We analytically and empirically evaluate the performance of the proposed algorithms. We compare the performance of the proposed algorithms with that of baseline algorithms. The experimental results on both synthetic and real graphs show that our proposed algorithms realize a compromise between effectiveness and efficiency, and, therefore provide practical solutions to the problem of incrementally sampling the large dynamic graphs.

Keywords

Markov Chain Forest Fire Degree Distribution Original Graph Markov Chain Monte Carlo Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
  3. 3.
    Ahmed, N.K., Neville, J., Kompella, R.: Space-efficient sampling from social activity streams. In: BigMine, pp. 53–60 (2012)Google Scholar
  4. 4.
    Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Berg, B.A.: Markov Chain Monte Carlo Simulations and Their Statistical Analysis: With Web-based Fortran Code. World Scientific Publishing Company (2004)Google Scholar
  6. 6.
    Desikan, P.K., Pathak, N., Srivastava, J., Kumar, V.: Incremental page rank computation on evolving graphs. In: WWW (Special Interest Tracks and Posters), pp. 1094–1095 (2005)Google Scholar
  7. 7.
    Fan, W., Li, J., Luo, J., Tan, Z., Wang, X., Wu, Y.: Incremental graph pattern matching. In: SIGMOD Conference, pp. 925–936 (2011)Google Scholar
  8. 8.
    Geweke, J.: Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bayesian Statistics, pp. 169–193 (1992)Google Scholar
  9. 9.
    Gionis, A., Mannila, H., Mielikäinen, T., Tsaparas, P.: Assessing data mining results via swap randomization. In: KDD, pp. 167–176 (2006)Google Scholar
  10. 10.
    Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Walking in facebook: A case study of unbiased sampling of osns. In: INFOCOM, pp. 2498–2506 (2010)Google Scholar
  11. 11.
    Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)MATHCrossRefGoogle Scholar
  12. 12.
    Hübler, C., Kriegel, H.-P., Borgwardt, K.M., Ghahramani, Z.: Metropolis algorithms for representative subgraph sampling. In: ICDM, pp. 283–292 (2008)Google Scholar
  13. 13.
    Kashtan, N., Itzkovitz, S., Milo, R., Alon, U.: Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs. Bioinformatics 20(11), 1746–1758 (2004)CrossRefGoogle Scholar
  14. 14.
    Leskovec, J., Faloutsos, C.: Sampling from large graphs. In: KDD, pp. 631–636 (2006)Google Scholar
  15. 15.
    Leskovec, J., Kleinberg, J.M., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. TKDD 1(1) (2007)Google Scholar
  16. 16.
    Lu, X., Bressan, S.: Sampling connected induced subgraphs uniformly at random. In: Ailamaki, A., Bowers, S. (eds.) SSDBM 2012. LNCS, vol. 7338, pp. 195–212. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Maiya, A.S., Berger-Wolf, T.Y.: Sampling community structure. In: WWW, pp. 701–710 (2010)Google Scholar
  18. 18.
    Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics 21(6), 1087–1092 (1953)CrossRefGoogle Scholar
  19. 19.
    Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network Motifs: Simple Building Blocks of Complex Networks. Science 298(5594), 824–827 (2002)CrossRefGoogle Scholar
  20. 20.
    Ribeiro, B.F., Towsley, D.F.: Estimating and sampling graphs with multidimensional random walks. In: Internet Measurement Conference, pp. 390–403 (2010)Google Scholar
  21. 21.
    Roditty, L., Zwick, U.: On dynamic shortest paths problems. Algorithmica 61(2), 389–401 (2011)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Sinclair, A.: Algorithms for Random Generation and Counting: A Markov Chain Approach (Progress in Theoretical Computer Science). Birkhäuser, Boston (1993)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xuesong Lu
    • 1
  • Tuan Quang Phan
    • 1
  • Stéphane Bressan
    • 1
  1. 1.School of ComputingNational University of SingaporeSingapore

Personalised recommendations