Efficient adaptive approximation algorithms in online social networks

Abstract

Online social networks (OSNs) have witnessed their prosperous developments in recent years. Based on the established relations among individuals in OSNs, ideas and opinions can be spread via a word-of-mouth effect. To exploit this effect, many companies have taken OSNs as the major advertising channels to promote their products, which has motivated substantial research on viral marketing. Among them, influence maximization, seed minimization, and profit maximization have been extensively studied in the past decades. These three problems are mainly studied in the non-adaptive setting in the literature, i.e., seed user selection phase does not involve any observations on influence propagation in reality. In this thesis, we extend profit maximization into a generalized version as target profit maximization and investigate these three problems in the adaptive setting, formulated as adaptive influence maximization, adaptive seed minimization, and adaptive target profit maximization respectively. Firstly, we study the adaptive influence maximization (IM) problem. Given a social network G and an integer k, the influence maximization problem asks for a seed set S of k nodes from G to maximize the expected number of nodes activated via an influence propagation. In the adaptive setting, the k seed nodes are selected in batches of equal size b, such that the i-th batch is identified after the actual influence results of the former i − 1 batches are observed. We propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of 1 − e α(ε−1) with high probability, where ε ∈ (0, 1) is a user-specified parameter and α = 1−(1−1/b) b is set by the batch size b. Our approach is based on a novel general framework AdaptGreedy which could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. In this regard, we design a novel non-adaptive IM algorithm called EPIC which not only provides strong expected approximation guarantee, but also i First and foremost, I would like to express my sincerest gratitude towards my supervisors, Prof. Xiaokui Xiao and Prof. Aixin Sun. It is their guidance of patience on my PhD research that makes the accomplishment of this thesis possible. In particular, Prof. Xiao's rigorous attitude, the pursuit of high standards, and unlimited enthusiasm for research have impressed and shaped me deeply. Prof. Sun, who comes from the hometown of Confucius in China, well interprets the charms of being a professor. It is his continuous help and care that support me forward. Their positive influence on me would be the priceless treasure for my future career and life. Then, I would like to thank my collaborators, especially Dr. Jing Tang. We have collaborated for two years. I learn so much from his great intelligence and experience on research such that I could conquer the challenges in my research.