Influence Maximization in Switching-Selection Threshold Models

  • Dimitris Fotakis
  • Thodoris Lykouris
  • Evangelos Markakis
  • Svetlana Obraztsova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)

Abstract

We study influence maximization problems over social networks, in the presence of competition. Our focus is on diffusion processes within the family of threshold models. Motivated by the general lack of positive results establishing monotonicity and submodularity of the influence function for threshold models, we introduce a general class of switching-selection threshold models where the switching and selection functions may also depend on the node activation history. This extension allows us to establish monotonicity and submodularity when (i) the switching function is linear and depends on the influence by all active neighbors, and (ii) the selection function is linear and depends on the influence by the nodes activated only in the last step. This implies a (1 − 1/e − ε)-approximation for the influence maximization problem in the competitive setting. On the negative side, we present a collection of counterexamples establishing that the restrictions above are essentially necessary. Moreover, we show that switching-selection threshold games with properties (i) and (ii) are valid utility games, and thus their Price of Anarchy is at most 2.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bharathi, S., Kempe, D., Salek, M.: Competitive influence maximization in social networks. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 306–311. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Borodin, A., Filmus, Y., Oren, J.: Threshold models for competitive influence in social networks. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 539–550. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD 2001, pp. 57–66.Google Scholar
  4. 4.
    Goldenberg, J., Libai, B., Muller, E.: Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters, 211–223 (2001)Google Scholar
  5. 5.
    Goyal, S., Kearns, M.: Competitive contagion in networks. In: STOC 2012, pp. 759–774 (2012)Google Scholar
  6. 6.
    Granovetter, M.S.: Threshold models of collective behavior. The American Journal of Sociology, 1420–1443 (1978)Google Scholar
  7. 7.
    He, X., Kempe, D.: Price of anarchy for the N-player competitive cascade game with submodular activation functions. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 232–248. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Kapralov, M., Post, I., Vondrák, J.: Online submodular welfare maximization: Greedy is optimal. In: SODA 2013, pp. 1216–1225 (2013)Google Scholar
  9. 9.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD 2003, pp. 137–146 (2013)Google Scholar
  10. 10.
    Mossel, E., Roch, S.: Submodularity of influence in social networks: From local to global. SIAM J. Comput., 2176–2188 (2010)Google Scholar
  11. 11.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions. Mathematical Programming, 265–294Google Scholar
  12. 12.
    Schelling, T.C.: Micromotives and Macrobehavior (1978)Google Scholar
  13. 13.
    Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In: FOCS 2002, pp. 416–425 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Dimitris Fotakis
    • 1
  • Thodoris Lykouris
    • 2
  • Evangelos Markakis
    • 3
  • Svetlana Obraztsova
    • 1
  1. 1.National Technical University of AthensAthensGreece
  2. 2.Cornell UniversityIthacaUSA
  3. 3.Athens University of Economics and BusinessAthensGreece

Personalised recommendations