Adaptive Seed Minimization for Diversified Influence Maximization

Yangguang Zhang, Qi Chen, Ji Shen, Qihao Shi, Can Wang

Abstract: The goal of the problem of maximizing influence in social networks is to trigger large-scale network chain influence spread by selecting seed users with greater influence. As a dual problem of maximizing impact, the seed minimization problem requires the minimum number of seed nodes to meet a given threshold. Most of the existing seed minimization algorithms consider non-adaptive settings, that is, select all seed nodes in the same batch without observing how they affect other users. Existing research mainly focuses on maximizing the number of activated nodes, but the diversity of activated nodes has been neglected. In this paper, the problem of diversity seed minimization in adaptive environment is studied. The goal of the problem is to select a minimum seed set so that the number and diversity of active nodes reach the target threshold. The seed node is selected from multiple batches, so the selection of a batch can use the actual impact information of the previous batch. This paper proposes an adaptive and effective diversity influence maximization algorithm, which provides the approximate guaranteed solution of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\frac{\ln ^2 \eta_\sigma+\ln ^2 \eta_d+2 \ln \eta_\sigma \ln \eta_d+2}{1-\epsilon}$</tex> in the expected time of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O\left(\left(\eta_\sigma+\frac{n}{D(V) \eta_d}\right) \frac{(n+m) \cdot \ln n}{\epsilon^2}\right)$</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta_{\sigma}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta_{d}$</tex> is the target influence and diversity diffusion, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\epsilon\in(0,1)$</tex> is the user specified parameter.