Several Practical Models and Their Approximate Solutions in Social Networks



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The online social platforms developed due to the popularity of the Internet and have become the mainstream way for daily communication as well as information spreading. The users and relationships between users in these social platforms can be abstracted by a social graph (social network). The most typical application in social networks is viral marketing, which takes the advantage of online advertisements to make information spread to more audiences in a short time. At the same time, we have to constrain the negative impact of misinformation spread. They can be formulated as combinatorial optimization problems in the directed graph, such as influence maximization, profit maximization, and rumor blocking. Influence spread can be characterized by different diffusion models. However, the existing models cannot portray the colorful real world. In this dissertation, we propose a series of new diffusion models, including a complementary products model, a multi-feature diffusion model, a k-hop collaborate game model, and an influence balancing model to adapt to some realistic applications in social networks, also study their related algorithmic problems. Because of their NP-hardness, we focus on designing efficient approximate algorithms. To overcome the #P-hardness of computing objective functions, we adopt the techniques of reverse influence sampling to improve efficiency without losing the approximation ratio.



Sampling (Statistics) -- Computer programs, Online social networks, Combinatorial optimization, Approximation algorithms