Advertisement

Limiting the Neighborhood: De-Small-World Network for Outbreak Prevention

  • Ruoming Jin
  • Yelong Sheng
  • Lin Liu
  • Xue-Wen Chen
  • NhatHai PhanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11917)

Abstract

In this work, we study a basic and practically important strategy to help prevent and/or delay an outbreak in the context of network: limiting the contact between individuals. In this paper, we introduce the average neighborhood size as a new measure for the degree of being small-world and utilize it to formally define the de-small-world network problem. We also prove the NP-hardness of the general reachable pair cut problem and propose a greedy edge betweenness based approach as the benchmark in selecting the candidate edges for solving our problem. Furthermore, we transform the de-small-world network problem as an OR-AND Boolean function maximization problem, which is also an NP-hardness problem. In addition, we develop a numerical relaxation approach to solve the Boolean function maximization and the de-small-world problem. Also, we introduce the short-betweenness, which measures the edge importance in terms of all short paths with distance no greater than a certain threshold, and utilize it to speed up our numerical relaxation approach. The experimental evaluation demonstrates the effectiveness and efficiency of our approaches.

References

  1. 1.
    Andersen, R., Chung, F., Lu, L.: Modeling the small-world phenomenon with local network flow. Internet Math. 2, 359–385 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177 (2001)CrossRefGoogle Scholar
  3. 3.
    Budak, C., Agrawal, D., El Abbadi, A.: Limiting the spread of misinformation in social networks. In: Proceedings of the 20th International Conference on World Wide Web, WWW 2011 (2011)Google Scholar
  4. 4.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Nat. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gregory, S.: Local betweenness for finding communities in networks. Technical report, University of Bristol, February 2008Google Scholar
  6. 6.
    Hager, W.W., Zhang, H.: A new active set algorithm for box constrained optimization. SIAM J. Optim. 17, 526–557 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jin, S., Bestavros, A.: Small-world characteristics of internet topologies and implications on multicast scaling. Comput. Netw. 50, 648–666 (2006)CrossRefGoogle Scholar
  8. 8.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2003, pp. 137–146 (2003)Google Scholar
  9. 9.
    Kleinberg, J.: The small-world phenomenon: an algorithmic perspective. In: 32nd ACM Symposium on Theory of Computing, pp. 163–170 (2000)Google Scholar
  10. 10.
    Leskovec, J., Horvitz, E.: Planetary-scale views on a large instant-messaging network. In: Proceedings of the 17th International Conference on World Wide Web, WWW 2008 (2008)Google Scholar
  11. 11.
    Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2007, pp. 420–429 (2007)Google Scholar
  12. 12.
    Milgram, S.: The small world problem. Psychol. Today 2, 60–67 (1967)Google Scholar
  13. 13.
    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 (2007)Google Scholar
  14. 14.
    Moore, C., Newman, M.E.J.: Epidemics and percolation in small-world networks. Phys. Rev. E 61, 5678–5682 (2000)CrossRefGoogle Scholar
  15. 15.
    Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66, 016128+ (2002)Google Scholar
  16. 16.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)CrossRefGoogle Scholar
  17. 17.
    Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2002, pp. 61–70 (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruoming Jin
    • 1
  • Yelong Sheng
    • 1
  • Lin Liu
    • 1
  • Xue-Wen Chen
    • 2
  • NhatHai Phan
    • 3
    Email author
  1. 1.Department of Computer ScienceKent State UniversityKentUSA
  2. 2.Department of EECSThe University of KansasLawrenceUSA
  3. 3.College of ComputingNew Jersey Institute of TechnologyNewarkUSA

Personalised recommendations