Influence Maximization in Independent Cascade Networks Based on Activation Probability Computation

Based on the concepts of <italic>“word-of-mouth”</italic> effect and <italic>viral marketing</italic>, the diffusion of an innovation may be triggered starting from a set of initial users. Estimating the influence spread is a preliminary step to determine a suitable or even optimal set of initial users to reach a given goal. In this paper, we focus on a stochastic model called the independent cascade model and compare a few approaches to compute activation probabilities of nodes in a social network, i.e., the probability that a user adopts the innovation. First, we propose the <italic>path method</italic> that computes the exact value of the activation probabilities but has high complexity. Second, an approximated method, called <italic>SSS-Noself</italic>, is obtained by the modification of the existing <italic>SteadyStateSpread</italic> algorithm, based on fixed-point computation, to achieve better accuracy. Finally, an efficient approach, also based on fixed-point computation, is proposed to compute the probability that a node is activated through a path of minimal length from the seed set. This algorithm, called <italic>SSS-Bounded-Path</italic> algorithm, can provide a lower bound for the computation of activation probabilities. Furthermore, these proposed approaches are applied to the influence maximization problem combined with the <italic>SelectTop</italic> <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> algorithm, the <italic>RankedReplace</italic> algorithm, and the greedy algorithm.

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