A General Stabilization Bound for Influence Propagation in Graphs
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Date
2020
Publication Type
Conference Paper
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yes
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Abstract
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.
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Publication status
published
External links
Book title
47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Volume
168
Pages / Article No.
90
Publisher
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Event
47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) (virtual)
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Minority process; Majority process
Organisational unit
03604 - Wattenhofer, Roger / Wattenhofer, Roger
Notes
Due to the Corona virus (COVID-19) the conference was conducted virtually.