Adaptive Greedy versus Non-adaptive Greedy for Influence Maximization

We consider the adaptive influence maximization problem: given a network and budget k, iteratively select k seeds in to maximize expected number of adopters. In full-adoption feedback model, after selecting each seed, seed-picker observes all resulting adoptions. myopic only whether neighbor chosen seed adopts. Motivated by extreme success greedy-based algorithms/heuristics for maximization, we propose concept greedy adaptivity gap, which compares performance algorithm its non-adaptive counterpart. Our first result shows that, submodular can perform up (1 − 1/e)-fraction worse than algorithm, that this ratio is tight. More specifically, on one side provide examples where (1−1/e) fraction four settings: both models independent cascade model linear threshold model. On other side, prove any cascade, always outputs 1/e)-approximation adoptions optimal choice. second general diffusion with feedback, outperform an unbounded factor. Finally, risk-free variant performs no algorithm.