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We study the adaptive influence maximization problem with myopic feedback under the independent cascade model: one sequentially selects k nodes as seeds one by one from a social network, and each selected seed returns the immediate neighbors it activates as the feedback available for by later selections, and the goal is to maximize the expected number of total activated nodes, referred as the influence spread. We show that the adaptivity gap, the ratio between the optimal adaptive influence spread and the optimal nonadaptive influence spread, is at most 4 and at least e/(e1), and the approximation ratios with respect to the optimal adaptive influence spread of both the nonadaptive greedy and adaptive greedy algorithms are at least \frac{1}{4}(1  \frac{1}{e}) and at most \frac{e^2 + 1}{(e + 1)^2} < 1  \frac{1}{e}. Moreover, the approximation ratio of the nonadaptive greedy algorithm is no worse than that of the adaptive greedy algorithm, when considering all graphs. Our result confirms a longstanding open conjecture of Golovin and Krause (2011) on the constant approximation ratio of adaptive greedy with myopic feedback, and it also suggests that adaptive greedy may not bring much benefit under myopic feedback.
Author Information
Binghui Peng (Columbia University)
Wei Chen (Microsoft Research)
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