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Stabilization Time in Weighted Minority Processes

Authors Pál András Papp, Roger Wattenhofer

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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 Weighted Minority Processes. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 54:1-54:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.54

Abstract

A minority process in a weighted graph is a dynamically changing coloring. Each node repeatedly changes its color in order to minimize the sum of weighted conflicts with its neighbors. We study the number of steps until such a process stabilizes. Our main contribution is an exponential lower bound on stabilization time. We first present a construction showing this bound in the adversarial sequential model, and then we show how to extend the construction to establish the same bound in the benevolent sequential model, as well as in any reasonable concurrent model. Furthermore, we show that the stabilization time of our construction remains exponential even for very strict switching conditions, namely, if a node only changes color when almost all (i.e., any specific fraction) of its neighbors have the same color. Our lower bound works in a wide range of settings, both for node-weighted and edge-weighted graphs, or if we restrict minority processes to the class of sparse graphs.

Subject Classification

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

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