Adaptive Influence Maximization

Influence maximization problem attempts to find a small subset of nodes that makes the expected influence spread maximized, which has been researched intensively before. They all assumed each user in seed set we select is activated successfully and then influence. However, real scenario, not users are willing be an influencer. Based on that, consider associated with probability can activate her as seed, attempt many times. In this paper, study adaptive multiple activations (Adaptive-IMMA) problem, where node iteration, observe whether she accepts if yes, wait diffusion process; If no, again higher cost or another seed. We model mathematically define it domain integer lattice. propose new concept, dr-submodularity, show our Adaptive-IMMA maximizing monotone dr-submodular function under knapsack constraint. Adaptive never covered by any existing studies. Thus, summarize its properties approximability comprehensively, non-trivial generalization analysis about submodularity. Besides, overcome difficulty estimate spread, combine greedy policy sampling techniques without losing approximation ratio but reducing time complexity. Finally, conduct experiments several datasets evaluate effectiveness efficiency proposed policies.