In this paper, we study the adaptivity gap of the influence maximization problem under independent cascade model when full-adoption feedback is available. Our main results are to derive upper bounds on several families of well-studied influence graphs, including in-arborescences, out-arborescences and bipartite graphs. Especially, we prove that the adaptivity gap for the in-arborescence is between [ e e−1 , 2e e−1 ] and for the out-arborescence, the gap is between [ e e−1 , 2]. These are the first constant upper bounds in the full-adoption feedback model. We provide several novel ideas to tackle with correlated feedback appearing in the adaptive stochastic optimization, which we believe to be of independent interests.
The adaptivity gap for the independent cascade model with full-adoption feedback, as well as the adaptivity gap for the linear threshold model with both feedback models, are still open problems, although there is some partial progress REF .
On Adaptivity Gaps of Influence Maximization under the Independent Cascade Model with Full Adoption Feedback
ArXiv
ArXiv
Computer Science