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Minimizing the influence spread over a network through node interception

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Abstract

We consider the problem of determining the optimal node interception strategy during influence propagation over a (directed) network \(G=(V,A)\). More specifically, this work aims to find an interception set \(D \subseteq V\) such that the influence spread over the remaining network \(G \backslash D\) under the linear threshold diffusion model is minimized. We prove its NP-hardness, even in the case when G is an undirected graph with unit edge weights. An exact algorithm based on integer linear programming and delayed constraint generation is proposed to determine the most critical nodes in the influence propagation process. Additionally, we investigate the technique of lifting inequalities of minimal activation sets. Experiments on the connected Watts-Strogatz small-world networks and real-world networks are also conducted to validate the effectiveness of our methodology.

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The data used in this paper have been previously detailed within the document. Additional data will be made available on reasonable request.

Notes

  1. https://www.gurobi.com/documentation/current/refman/parameters.html.

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Authors and Affiliations

  1. Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Shunyu Yao, Neng Fan & Pavlo Krokhmal

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  1. Shunyu Yao
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  2. Neng Fan
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  3. Pavlo Krokhmal
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Correspondence to Neng Fan.

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Yao, S., Fan, N. & Krokhmal, P. Minimizing the influence spread over a network through node interception. Optim Lett (2024). https://doi.org/10.1007/s11590-024-02117-w

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