Influence Maximization in Switching-Selection Threshold Models
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.
Unable to display preview. Download preview PDF.
- 3.Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD 2001, pp. 57–66.Google Scholar
- 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.Goyal, S., Kearns, M.: Competitive contagion in networks. In: STOC 2012, pp. 759–774 (2012)Google Scholar
- 6.Granovetter, M.S.: Threshold models of collective behavior. The American Journal of Sociology, 1420–1443 (1978)Google Scholar
- 8.Kapralov, M., Post, I., Vondrák, J.: Online submodular welfare maximization: Greedy is optimal. In: SODA 2013, pp. 1216–1225 (2013)Google Scholar
- 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.Mossel, E., Roch, S.: Submodularity of influence in social networks: From local to global. SIAM J. Comput., 2176–2188 (2010)Google Scholar
- 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.Schelling, T.C.: Micromotives and Macrobehavior (1978)Google Scholar
- 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