文章基本信息

标题：A General Stabilization Bound for Influence Propagation in Graphs
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作者：P{'a}l Andr{'a}s Papp ; Roger Wattenhofer
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：90:1-90:15
DOI：10.4230/LIPIcs.ICALP.2020.90
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the stabilization time of a wide class of processes on graphs, in which each node can only switch its state if it is motivated to do so by at least a (1+Î»)/2 fraction of its neighbors, for some 0 < Î» < 1. Two examples of such processes are well-studied dynamically changing colorings in graphs: in majority processes, nodes switch to the most frequent color in their neighborhood, while in minority processes, nodes switch to the least frequent color in their neighborhood. We describe a non-elementary function f(Î»), and we show that in the sequential model, the worst-case stabilization time of these processes can completely be characterized by f(Î»). More precisely, we prove that for any Îµ > 0, O(n^(1+f(Î»)+Îµ)) is an upper bound on the stabilization time of any proportional majority/minority process, and we also show that there are graph constructions where stabilization indeed takes Î©(n^(1+f(Î»)-Îµ)) steps.
关键词：Minority process; Majority process