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Maximizing Influence of Leaders in Social Networks
arXiv - CS - Computers and Society Pub Date : 2021-06-11 , DOI: arxiv-2106.06128
Xiaotian Zhou, Zhongzhi Zhang

The operation of adding edges has been frequently used to the study of opinion dynamics in social networks for various purposes. In this paper, we consider the edge addition problem for the DeGroot model of opinion dynamics in a social network with $n$ nodes and $m$ edges, in the presence of a small number $s \ll n$ of competing leaders with binary opposing opinions 0 or 1. Concretely, we pose and investigate the problem of maximizing the equilibrium overall opinion by creating $k$ new edges in a candidate edge set, where each edge is incident to a 1-valued leader and a follower node. We show that the objective function is monotone and submodular. We then propose a simple greedy algorithm with an approximation factor $(1-\frac{1}{e})$ that approximately solves the problem in $O(n^3)$ time. Moreover, we provide a fast algorithm with a $(1-\frac{1}{e}-\epsilon)$ approximation ratio and $\tilde{O}(mk\epsilon^{-2})$ time complexity for any $\epsilon>0$, where $\tilde{O}(\cdot)$ notation suppresses the ${\rm poly} (\log n)$ factors. Extensive experiments demonstrate that our second approximate algorithm is efficient and effective, which scales to large networks with more than a million nodes.

中文翻译:

最大限度地发挥领导者在社交网络中的影响力

出于各种目的,添加边的操作经常被用于研究社交网络中的意见动态。在本文中,我们考虑了具有 $n$ 个节点和 $m$ 条边的社交网络中意见动态的 DeGroot 模型的边添加问题,其中存在少量 $s \ll n$ 与二进制竞争的领导者反对意见 0 或 1。具体而言,我们通过在候选边集中创建 $k$ 条新边来提出并研究最大化均衡总体意见的问题,其中每条边都与一个 1 值的领导者和一个跟随者节点相关。我们表明目标函数是单调和子模块的。然后,我们提出了一个简单的贪心算法,其近似因子 $(1-\frac{1}{e})$ 可以在 $O(n^3)$ 时间内近似解决问题。而且,我们为任何 $\ 提供了一个具有 $(1-\frac{1}{e}-\epsilon)$ 近似比和 $\tilde{O}(mk\epsilon^{-2})$ 时间复杂度的快速算法epsilon>0$,其中 $\tilde{O}(\cdot)$ 符号抑制了 ${\rm poly} (\log n)$ 因子。大量实验表明,我们的第二个近似算法高效且有效,可扩展到具有超过一百万个节点的大型网络。
更新日期:2021-06-14
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