Non-submodular model for group profit maximization problem in social networks

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...

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Published in:Computational social networks Vol. 8; no. 1
Main Authors: Zhu, Jianming, Ghosh, Smita, Wu, Weili, Gao, Chuangen
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.01.2021
Springer Nature B.V
Subjects:
Algorithms
Data-driven Science
Database Management
Election results
Elections
Industrial and Production Engineering
Industrial Organization
Lower bounds
Mathematical Models of Cognitive Processes and Neural Networks
Mathematics
Mathematics and Statistics
Maximization
Media Sociology
Modeling and Theory Building
Optimization
Presidential elections
Profit maximization
Social networks
Upper bounds
Group profit maximization
Social networks
Submodular–modular algorithm
Non-submodular
ISSN:2197-4314, 2197-4314
Online Access:Get full text
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Summary: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 β 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.
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ISSN:2197-4314
2197-4314
DOI:10.1186/s40649-020-00085-6