eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-04-29
7:1
7:17
10.4230/LIPIcs.SAND.2022.7
article
Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem
Berenbrink, Petra
1
Biermeier, Felix
1
Hahn, Christopher
1
Kaaser, Dominik
1
https://orcid.org/0000-0002-2083-7145
Universität Hamburg, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol221-sand2022/LIPIcs.SAND.2022.7/LIPIcs.SAND.2022.7.pdf
Population Protocols
Phase Clocks
Loose Self-stabilization
Clock Synchronization
Majority
Adaptive