文章基本信息
- 标题：A General Stabilization Bound for Influence Propagation in Graphs
- 本地全文：下载
- 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+λ)/2 fraction of its neighbors, for some 0 < λ < 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(λ), and we show that in the sequential model, the worst-case stabilization time of these processes can completely be characterized by f(λ). More precisely, we prove that for any ε > 0, O(n^(1+f(λ)+ε)) 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 Ω(n^(1+f(λ)-ε)) steps.
- 关键词：Minority process; Majority process
