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Stabilization Time in Minority Processes

Authors Pál András Papp, Roger Wattenhofer

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LIPIcs.ISAAC.2019.43.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. Stabilization Time in Minority Processes. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ISAAC.2019.43

Abstract

We analyze the stabilization time of minority processes in graphs. A minority process is a dynamically changing coloring, where each node repeatedly changes its color to the color which is least frequent in its neighborhood. First, we present a simple Omega(n^2) stabilization time lower bound in the sequential adversarial model. Our main contribution is a graph construction which proves a Omega(n^(2-epsilon)) stabilization time lower bound for any epsilon>0. This lower bound holds even if the order of nodes is chosen benevolently, not only in the sequential model, but also in any reasonable concurrent model of the process.

Subject Classification

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

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