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Risk-Averse Influence Maximization

A computational investigation by genetic algorithm framework

Abstract

The top k-influencers problem, as a social influence maximization (SIM) problem, seeks out the best k actors, called the seed set, in a network with the greatest expected Influence Spread (IS). This problem is formulated as a mean-maximization of the IS with no consideration for the variance of the IS. Consequently, it is a risk-blind influence maximization (RBIM) problem. The variance minimization problem has a considerable tendency toward trivial solutions in the absence of a known exogenous threshold of the IS, which makes the formulation ineffective. As an alternative strategy to overcome the trivial solution challenge, risk-averse influence maximization (RAIM) is being investigated and compared empirically with RBIM based on theoretical findings from the literature. RAIM searches for the best k actors under a known diffusion process, whose conditional value-at-risk (CVaR) measure of the IS is maximized. RAIM lacks an approximation algorithm due to the absence of a proven submodularity feature for CVaR. Moreover, no metaheuristic framework was tuned under all of the IC, WC, LT, and TR diffusion models, despite numerous algorithmic contributions to RBIM. Thus, a Genetic Algorithm Framework for Influence Maximization (GAFIM) is proposed by drawing inspiration from the genetic algorithms proposed for RBIM but under all of the IC, WC, LT, and TR diffusion models. A novel approach to tuning GAFIM has been developed employing a community detection algorithm and applied to RAIM and RBIM. Based on the tuning results, the seed set size has a remarkable effect on GAFIM’s performance and highlights its superiority over the algorithms it was inspired by. Furthermore, a comparison to the closest genetic algorithm published in the literature demonstrates that GAFIM outperforms it by a factor of at least 20 in terms of efficiency while achieving a higher quality result. Having completed the quality investigation of GAFIM with satisfactory results, the comparison experiments support intriguing distinctions between RAIM and RBIM in the dominance factor, dominance rate, and dominance mutuality. The variance of the IS and the propagation time/median of the IS prepare the dominance factor(s) for RAIM/RBIM. According to the results, the significant dominance rates (48% vs. 65%), the unreciprocated dominance pattern in dominating the other problem in its dominance area (66% vs. 91%), the complete dominance pattern in dominating without being dominated (9% vs. 34%), and being nondominated (35% vs. 52%) are not as probable for RBIM as for RAIM.

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Data availability

The datasets analysed during the current study are available in two repositories: (1) The Pajek Datasets (2006) [54] repository: http://vlado.fmf.uni-lj.si/pub/networks/data/. (2) The Network Data Repository with interactive graph analytics and visualization [60]: http://networkrepository.com.

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Correspondence to Mohammad Fathian.

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NasehiMoghaddam, S., Fathian, M. & Amiri, B. Risk-Averse Influence Maximization. J Supercomput (2022). https://doi.org/10.1007/s11227-022-04731-w

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Keywords

  • Influence spread (IS) values variation
  • Risk-Averse Influence Maximization (RAIM)
  • Risk-Blind Influence Maximization (RBIM)
  • Conditional Value at Risk (CVaR)
  • Genetic Algorithm Framework for Influence Maximization (GAFIM)
  • Tuning by community detection