Target users' activation probability maximization with different seed set constraints in social networks

Abstract

Influence Maximization (IM) over the online social networks have been widely explored in recent years, which selects a seed set from nodes in the network using a limited budget such that the expected number of nodes influenced by the seed set is maximized. However, how to activate a considered set of targeting users T, e.g., selling a product to a specific target group, is a more practical problem. To address this problem, we respectively propose the Target Users' Activation Probability Maximization with Constraint (TUAPM-WC) problem and the Target Users' Activation Probability Maximization without Constraint (TUAPM-WOC) problem, i.e., to select a seed set S with/without size constraints such that the activation probabilities of the target users in T are maximized. Considering that the influence will decay during information propagation, we propose a novel and practical Influence Decay Model (IDM) as the information diffusion model.Based on the IDM, we show that the TUAPM-WC and the TUAPM-WOC problems are NP-hard. We also prove that the objective functions of TUAPM-WC and TUAPM-WOC problems are monotone non-decreasing and submodular. On one hand, we employ a Double Greedy Algorithm (DGA) to guarantee a (1/3)-approximation ratio for TUAPM-WOC problem when |S| is unconstrained. On the other hand, we propose a series of algorithms to solve the TUAPM-WC when |S|≤b, where b is a positive integer. More specifically, we provide a (1−1/e)-approximation Basic Greedy Algorithm (BGA). Furthermore, a speed-up Scalable Algorithm (SA) is proposed for online large social networks. Finally, we run our algorithms by simulations on synthetic and real-life social networks to evaluate the effectiveness and efficiency of the proposed algorithms. Experimental results validate our algorithms' superior to the comparison algorithms.