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Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem

Authors Petra Berenbrink, Felix Biermeier, Christopher Hahn, Dominik Kaaser

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Petra Berenbrink
  • Universität Hamburg, Germany
Felix Biermeier
  • Universität Hamburg, Germany
Christopher Hahn
  • Universität Hamburg, Germany
Dominik Kaaser
  • Universität Hamburg, Germany

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Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser. Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SAND.2022.7

Abstract

We present a loosely-stabilizing phase clock for population protocols. In the population model we are given a system of n identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires O(log n) states. It runs forever and is, at any point of time, in a synchronous state w.h.p. When started in an arbitrary configuration, it recovers rapidly and enters a synchronous configuration within O(n log n) interactions w.h.p. Once the clock is synchronized, it stays in a synchronous configuration for at least poly(n) parallel time w.h.p.
We use our clock to design a loosely-stabilizing protocol that solves the adaptive variant of the majority problem. We assume that the agents have either opinion A or B or they are undecided and agents can change their opinion at a rate of 1/n. The goal is to keep track which of the two opinions is (momentarily) the majority. We show that if the majority has a support of at least Ω(log n) agents and a sufficiently large bias is present, then the protocol converges to a correct output within O(n log n) interactions and stays in a correct configuration for poly(n) interactions, w.h.p.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • Population Protocols
  • Phase Clocks
  • Loose Self-stabilization
  • Clock Synchronization
  • Majority
  • Adaptive

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References

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