Maximizing influence-based group shapley centrality

A key problem in network analysis is the influence maximization problem, which consists of finding a set S of at most k seed users in a social network, such that the spread of information from S is maximized. We investigate the problem of choosing the best set of seeds when there exists an unknown pre-existing set of seed nodes. Our work extends the one of Chen and Teng (WWW'17) who introduced the so-called Shapley centrality of a node to measure the efficiency of nodes acting as seeds within a pre-existing but unknown set of seeds. We instead consider the question: Which set of cardinality k to target in this kind of scenario? The resulting optimization problem reveals very challenging, that is, assuming common computational complexity conjectures, we obtain strong hardness of approximation results. Nevertheless,we design a greedy algorithm which achieves an approximation factor of 1-1/e/k - ∈ for any ∈ > 0, showing that not all is lost in settings where k is bounded.