Abstract
We address the problem of influence maximization within the framework of the linear threshold model, focusing on its comparison to the independent cascade model. Previous research has predominantly concentrated on the independent cascade model, providing various bounds on the adaptivity gap in influence maximization. For the case of a (directed) tree (in-arborescence and out-arborescence), [CP19] and [DPV23] have established constant upper and lower bounds for the independent cascade model.
However, the adaptivity gap of this problem on the linear threshold model is not so extensively studied as on the independent cascade model. In this study, we present constant upper bounds for the adaptivity gap of the linear threshold model on trees. Our approach builds upon the original findings within the independent cascade model and employs a reduction technique to deduce an upper bound of \(\frac{4e^2}{e^2-1}\) for the in-arborescence scenario. For out-arborescence, the equivalence between the two models reveals that the adaptivity gap under the linear threshold model falls within the range of \([\frac{e}{e-1},2]\), as demonstrated in [CP19] under the independent cascade model.
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Notes
- 1.
Another commonly considered model is called the myopic feedback model, where only one iteration of the spread can be observed.
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Acknowledgements
The research of K. Yang is supported by the NSFC grant No. 62102253. Y. Tao, S. Wang and K. Yang sincerely thank the anonymous reviewers for their helpful feedback. Y. Tao, S. Wang and K. Yang also want to express the gratitude to Panfeng Liu and Biaoshuai Tao for their insightful suggestions during the composition of this paper.
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Tao, Y., Wang, S., Yang, K. (2023). Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_12
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