Efficient Targeted Influence Maximization Based on Multidimensional Selection in Social Networks - Jing, Dong; Liu, Ting (Frontiers in Physics, 2021)
The influence maximization problem over social networks has become a popular research problem, since it has many important practical applications such as online advertising, virtual market and so on. General influence maximization problem is defined over the whole network, whose intuitive aim is to find a seed node set with size at most $k$ in order to affect as many as nodes in the network. However, in real applications, it is commonly required that only special nodes (target) in the network are expected to be influenced, which can use the same cost of placing seed nodes but influence more targeted nodes really needed. Some research efforts have provided solutions for the corresponding targeted influence maximization problem (TIM for short). However, there are two main drawbacks of previous works focusing on the TIM problem. First, some works focusing on the case the targets are given arbitrarily make it hard to achieve efficient performance guarantee required by real applications. Second, some previous works studying the TIM problems by specifying the target set in a probabilistic way is not proper for the case that only exact target set is required. In this paper, we study the Multidimensional Selection based Targeted Influence Maximization problem, MSTIM for short. First, the formal definition of the problem is given based on a brief and expressive fragment of general multi-dimensional queries. Then, a formal theoretical analysis about the computational hardness of the MSTIM problem shows that even for a very simple case that the target set specified is 1 larger than the seed node set, the MSTIM problem is still NP-hard. Then, the basic framework of RIS (short for Reverse Influence Sampling) is extended and shown to have a $1-1/e-ε$ approximation ratio when a sampling size is satisfied. To satisfy the efficiency requirements, an index-based method for the MSTIM problem is proposed, which utilizes the ideas of reusing previous results, exploits the covering relationship between queries and achieves an efficient solution for MSTIM. Finally, the experimental results on real datasets show that the proposed method is indeed rather efficient.