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# Loosely-stabilizing phase clocks and The Adaptive Majority Problem

Publikationstyp

Conference Paper

Publikationsdatum

2022-04

Sprache

English

Author

First published in

Number in series

221

Article Number

7

Citation

1st Symposium on Algorithmic Foundations of Dynamic Networks : SAND 2022, March 28-30, 2022, virtual conference. - (Leibniz International Proceedings in Informatics, LIPIcs ; vol. 221). - Art. no. 7 - (2022)

Contribution to Conference

Publisher DOI

Scopus ID

Publisher

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

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.