Influence Maximization for Fixed Heterogeneous Thresholds.

Influence Maximization is a NP-hard problem of selecting the optimal set of influencers in a network. Here, we propose two new approaches to influence maximization based on two very different metrics. The first metric, termed Balanced Index (BI), is fast to compute and assigns top values to two kinds of nodes: those with high resistance to adoption, and those with large out-degree. This is done by linearly combining three properties of a node: its degree, susceptibility to new opinions, and the impact its activation will have on its neighborhood. Controlling the weights between those three terms has a huge impact on performance. The second metric, termed Group Performance Index (GPI), measures performance of each node as an initiator when it is a part of randomly selected initiator set. In each such selection, the score assigned to each teammate is inversely proportional to the number of initiators causing the desired spread. These two metrics are applicable to various cascade models; here we test them on the Linear Threshold Model with fixed and known thresholds. Furthermore, we study the impact of network degree assortativity and threshold distribution on the cascade size for metrics including ours. The results demonstrate our two metrics deliver strong performance for influence maximization.