In this paper, we study the adaptivity gap of the influence maximization problem under the 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-arborescences is between [e/(e-1), 2e/(e-1)], and for the out-arborescences the gap is between [e/(e-1), 2]. These are the first constant upper bounds in the full-adoption feedback model. Our analysis provides several novel ideas to tackle the correlated feedback appearing in adaptive stochastic optimization, which may be of independent interest.
@InProceedings{chen_et_al:LIPIcs.ISAAC.2019.24, author = {Chen, Wei and Peng, Binghui}, title = {{On Adaptivity Gaps of Influence Maximization Under the Independent Cascade Model with Full-Adoption Feedback}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {24:1--24:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.24}, URN = {urn:nbn:de:0030-drops-115208}, doi = {10.4230/LIPIcs.ISAAC.2019.24}, annote = {Keywords: Adaptive influence maximization, adaptivity gap, full-adoption feedback} }
Feedback for Dagstuhl Publishing