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Non-submodular model for group profit maximization problem in social networks
Computational Social Networks Pub Date : 2021-01-07 , DOI: 10.1186/s40649-020-00085-6
Jianming Zhu , Smita Ghosh , Weili Wu , Chuangen Gao

In social networks, there exist many kinds of groups in which people may have the same interests, hobbies, or political orientation. Sometimes, group decisions are made by simply majority, which means that most of the users in this group reach an agreement, such as US Presidential Elections. A group is called activated if $$\beta$$ percent of users are influenced in the group. Enterprise will gain income from all influenced groups. Simultaneously, to propagate influence, enterprise needs pay advertisement diffusion cost. Group profit maximization (GPM) problem aims to pick k seeds to maximize the expected profit that considers the benefit of influenced groups with the diffusion cost. GPM is proved to be NP-hard and the objective function is proved to be neither submodular nor supermodular. An upper bound and a lower bound which are difference of two submodular functions are designed. We propose a submodular–modular algorithm (SMA) to solve the difference of two submodular functions and SMA is shown to converge to a local optimal. We present an randomized algorithm based on weighted group coverage maximization for GPM and apply sandwich framework to get theoretical results. Our experiments verify the efficiency of our methods.

中文翻译:

社交网络中群体利润最大化问题的非子模模型

在社交网络中,存在许多人群可能具有相同兴趣,爱好或政治倾向的群体。有时,小组决策仅由多数人做出,这意味着该小组中的大多数用户都达成了协议,例如美国总统选举。如果$$ \ beta $$%的用户影响该组,则该组称为激活。企业将从所有受影响的群体中获得收入。同时,为了传播影响力,企业需要付出广告传播成本。小组利润最大化(GPM)问题旨在选择k粒种子以最大化预期利润,该期望利润考虑了受影响群体的利益与扩散成本。GPM被证明是NP-hard,目标函数被证明既不是亚模也不是超模。设计了两个亚模函数之差的上限和下限。我们提出了一种亚模-模块化算法(SMA)来解决两个亚模函数的差异,并且SMA被证明收敛于局部最优。我们提出了一种基于加权组覆盖最大化的GPM随机算法,并应用三明治框架来获得理论结果。我们的实验验证了我们方法的有效性。
更新日期:2021-01-07
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