Diversity is a crucial criterion in many ranking and mining tasks. In this paper, we study how to incorporate node diversity into influence maximization (IM). We consider diversity as a reverse measure of the average similarity between selected nodes, which can be specified using node embedding or community detection results. Our goal is to identify a set of nodes which are simultaneously influential and diverse. Three most commonly used utilities in economics (i.e., Perfect Substitutes, Perfect Complements, and Cobb-Douglas) are proposed to jointly model influence spread and diversity as two factors. We formulate diversified IM as two optimization problems (i.e., a budgeted version and an unconstrained version) of these utilities and show their NP-hardness. Then we prove the utilities are all (non-monotonic and) submodular, and it is impossible to find a monotonic utility modeling the two factors in a reasonable way. Various algorithms with theoretical guarantees are proposed to solve diversified IM in the two settings. Experimental results show that our diversified IM framework outperforms other natural heuristics, such as embedding, diversified ranking and traditional IM, both in utility maximization and result diversification.

本文从博弈的角度研究影响最大化问题，提出了一个协调博弈模型，并在该模型下研究了影响最大化的难度和贪心算法的逼近保证。实验结果表明，优化后的算法比其他启发式算法快三个数量级，并且大大优于原始贪心方法。

社交网络中的Top-K影响节点：游戏视角