Before revision:  Nevertheless, we show that a simple greedy allocation can ensure a (1-1/e-\epsilon) -approximation to the optimum . To the best of our knowledge, this is the first instance where for a non-submodular objective in the context of viral marketing, such a high approximation ratio is achieved. We provide the analysis of this result, which is highly nontrivial and along the way we give a solution to the prefix-preserving influence maximization problem, which could be of independent interest. With extensive\textsf{  experiments on real and synthetic datasets, we show that our algorithm significantly outperforms all the baselines.
After revision:  Nevertheless, we show that a simple greedy allocation can ensure a (1-1/e-\epsilon) of the optimum expected social welfare. We develop\textsf{ experiments on real and synthetic datasets, we show that our algorithm significantly outperforms all the baselines.