Better Approximation Algorithms for Technology Diffusion

  • Jochen Könemann
  • Sina Sadeghian
  • Laura Sanità
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


Motivated by cascade effects arising in network technology upgrade processes in the Internet, Goldberg and Liu [SODA, 2013] recently introduced the following natural technology diffusion problem. Given a graph G = (V,E), and thresholds θ(v), for all v ∈ V. A vertex u activates if it is adjacent to a connected component of active nodes of size at least θ(v). The goal is to find a seed set \(\mathcal{A}\) whose initial activation would trigger a cascade activating the entire graph.

Goldberg and Liu presented an algorithm for this problem that returns a seed set of size O(rl log(n)) times that of an optimum seed set, where r is the diameter of the given graph, and l is the number of distinct thresholds used in the instance. We improve upon this result by presenting an O( min {r,l} log(n))-approximation algorithm. Our algorithm is simple and combinatorial, in contrast with the previous approach that is based on randomized rounding applied to the solution of a linear program.


Approximation Algorithms Technology Diffusion Combinatorial Optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: Proceedings of the Knowledge Discovery and Data Mining, pp. 57–66 (2001)Google Scholar
  2. 2.
    Easley, D.A., Kleinberg, J.M.: Networks, Crowds, and Markets - Reasoning About a Highly Connected World. Cambridge University Press (2010)Google Scholar
  3. 3.
    Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45 (1998)Google Scholar
  4. 4.
    Gill, P., Schapira, M., Goldberg, S.: Let the market drive deployment: a strategy for transitioning to bgp security. SIGCOMM Comput. Commun. Rev. 41(4), 14–25 (2011)CrossRefGoogle Scholar
  5. 5.
    Goldberg, S., Liu, Z.: Technology diffusion in communication networks. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pp. 233–240 (2013)Google Scholar
  6. 6.
    Goldenberg, J., Libai, B., Muller, E.: Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing letters 12(3), 211–223 (2001)CrossRefGoogle Scholar
  7. 7.
    Granovetter, M.: Threshold models of collective behavior. American Journal of Sociology, 1420–1443 (1978)Google Scholar
  8. 8.
    Guérin, R., Hosanagar, K.: Fostering ipv6 migration through network quality differentials. ACM SIGCOMM Computer Communication Review 40(3), 17–25 (2010)CrossRefGoogle Scholar
  9. 9.
    Jackson, M.: Social and Economic Networks. Princeton University Press (2008)Google Scholar
  10. 10.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings, Knowledge Discovery and Data Mining, KDD 2003, pp. 137–146 (2003)Google Scholar
  11. 11.
    Könemann, J., Sadeghian, S., Sanità, L.: An LMP O(log n)-approximation algorithm for node weighted prize collecting Steiner tree. Technical Report 1302.2127, arXiv (2013)Google Scholar
  12. 12.
    Metcalfe, B.: Metcalfe’s law: A network becomes more valuable as it reaches more users. In: InfoWorld (1995)Google Scholar
  13. 13.
    Moss, A., Rabani, Y.: Approximation algorithms for constrained node weighted steiner tree problems. SIAM J. Comput. 37(2), 460–481 (2007)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.: Algorithmic Game Theory. Cambridge University Press (2007)Google Scholar
  15. 15.
    Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proceedings of the Knowledge Discovery and Data Mining (2002)Google Scholar
  16. 16.
    Schelling, T.: Micromotives and Macrobehavior. Norton (1978)Google Scholar
  17. 17.
    Wolsey, L.A.: An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica 2(4), 385–393 (1982)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jochen Könemann
    • 1
  • Sina Sadeghian
    • 1
  • Laura Sanità
    • 1
  1. 1.Faculty of Mathematics, Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations