A general greedy approximation algorithm for finding minimum positive influence dominating sets in social networks

In social networks, the minimum positive influence dominating set (MPIDS) problem is NP-hard, which means it is unlikely to be solved precisely in polynomial time. For the purpose of efficiently solving this problem, greedy approximation algorithms seem appealing because they are fast and can provide guaranteed solutions. In this paper, based on the classic greedy algorithm for cardinality submodular cover, we propose a general greedy approximation algorithm (GGAA) for the MPIDS problem, which uses a generic real-valued submodular potential function, and enjoys a provable approximation guarantee under a wide condition. Two existing greedy algorithms, one of which is unknown for having an approximation ratio, both can be viewed as the specific versions of GGAA, and are shown to enjoy an approximation guarantee of the same order. Applying the framework of GGAA, we also design two new greedy approximation algorithms with fractional submodular potential functions. All these greedy algorithms are O(lnα ) -approximations where α is the maximum node degree of the network graph, while it is shown experimentally that these two new algorithms can yield better solutions on typical real social network instances. In this work, as a by-product, we achieve a new approximation ratio of the classic greedy algorithm for cardinality submodular cover, which slightly generalizes two existing results.