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A General Stabilization Bound for Influence Propagation in Graphs

Authors Pál András Papp, Roger Wattenhofer

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LIPIcs.ICALP.2020.90.pdf
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Pál András Papp
  • ETH Zürich, Switzerland
Roger Wattenhofer
  • ETH Zürich, Switzerland

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Pál András Papp and Roger Wattenhofer. A General Stabilization Bound for Influence Propagation in Graphs. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 90:1-90:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ICALP.2020.90

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph coloring
  • Theory of computation → Distributed computing models
  • Theory of computation → Self-organization
Keywords
  • Minority process
  • Majority process

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