Randomized rumor spreading processes diffuse information on an undirected graph and have been widely studied. In this work, we present a generic framework for analyzing a broad class of such processes on regular graphs. Our analysis is protocol-agnostic, as it only requires the expected proportion of newly informed vertices in each round to be bounded, and a natural negative correlation property. This framework allows us to analyze various protocols, including PUSH, PULL, and PUSH-PULL, thereby extending prior research. Unlike previous work, our framework accommodates message failures at any time t ≥ 0 with a probability of 1-q(t), where the credibility q(t) is any function of time. This enables us to model real-world scenarios in which the transmissibility of rumors may fluctuate, as seen in the spread of "fake news" and viruses. Additionally, our framework is sufficiently broad to cover dynamic graphs.
@InProceedings{out_et_al:LIPIcs.ITCS.2024.86, author = {Out, Charlotte and Rivera, Nicol\'{a}s and Sauerwald, Thomas and Sylvester, John}, title = {{Rumors with Changing Credibility}}, booktitle = {15th Innovations in Theoretical Computer Science Conference (ITCS 2024)}, pages = {86:1--86:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-309-6}, ISSN = {1868-8969}, year = {2024}, volume = {287}, editor = {Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.86}, URN = {urn:nbn:de:0030-drops-196149}, doi = {10.4230/LIPIcs.ITCS.2024.86}, annote = {Keywords: Rumor spreading, epidemic algorithms, "fake news"} }
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