Finding effectors in social networks

Assume a network (V,E) where a subset of the nodes in V are active. We consider the problem of selecting a set of k active nodes that best explain the observed activation state, under a given information-propagation model. We call these nodes effectors. We formally define the k-Effectors problem and study its complexity for different types of graphs. We show that for arbitrary graphs the problem is not only NP-hard to solve optimally, but also NP-hard to approximate. We also show that, for some special cases, the problem can be solved optimally in polynomial time using a dynamic-programming algorithm. To the best of our knowledge, this is the first work to consider the k-Effectors problem in networks. We experimentally evaluate our algorithms using the DBLP co-authorship graph, where we search for effectors of topics that appear in research papers.