The problem: Information competition finds its application in many scenarios (e.g., the spread of rumors and their refutations). A flurry of work has been dedicated to revealing the underlying competing dynamics but reaches different conclusions: "the winner will take all" and "the winner will not take all". Both findings have their evidences in the real world (e.g., Facebook vs. Myspace, Android vs. iOS). Then, will the winner take all?

Our solution: To answer this question, we make a comprehensive study by considering two more factors: the incompleteness of the given network structure and the effect of information overload on user behavior. To this end, we first apply the well-known Network Embedding technique in machine learning to predict possible latent links and then take account of users’ information processing strategies under information overload.

    On this basis, we capture the competing dynamics by difference equations. To handle these equations, we transform them into ordinary differential equations (ODEs) by showing that the gap between the two forms are infinitesimals. Finally, we reply to the controversy by giving the condition under which the winner will take all.

The problem: Influence maximization (IM) is a fundamental problem in network study, which is also closely related to stochastic optimization, operation researches etc. Specifically, given a social network , a budget , the IM problem tries to select users (called seeds) to trigger the largest cascade of information.

    Due to users' privacy concern etc., the selection of seeds is often limited to a small subset of users . Such limitation would significantly impair the spread of influence.

Our solution: To approach this problem, we are lucky to prove the existence of a basic network structure, called set-wise friendship paradox, in all networks, that is, the neighbors of users are more influential than themselves. Thus, we are inspired to devise a two-stage framework to recruit the neighbors.

    Under this idea, we propose both non-adaptive and adaptive algorithms. In the non-adaptive algorithm, we design a two-stage coordinate descent framework which will finally converge. In the adaptive case, a series of greedy algorithms are proposed with constant approximation ratios by leveraging the submodular/adaptive submodular property. And the best algorithm achieves a larger ratio (0.468) than the state-of-the-art (0.399). Finally, extensive experiments in million-scale networks are carried out, validating the superiority of our algorithms.

The problem: Content transmission is a prevalent form of user interaction, where transmission time acts as one of the most concerned metric in user experience. It is frequently overlooked that real networks are evolving over time with structural changes, which would significantly affect the transmission efficiency. Then, what is the transmission time in evolving networks?

Our solution: We reveal the mesoscopic structure of the evolving network by deriving the upper bound and lower bound of the neighborhood size. On this basis, we strategically set the transmission parameters to guarantee that each user would find a holder for request with high probability. Finally, we derive the upper bound and lower bound of the transmission time in both static case and mobile case. Moreover, a general result about probability analysis is derived when analyzing the mobile case. Summarizing the results, we find that the transmission in evolving networks is actually faster than the non-evolving ones.