Loosely-stabilizing phase clocks and The Adaptive Majority Problem

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.

Subjects

Adaptive

Clock Synchronization

Loose Self-stabilization

Majority

Phase Clocks

Population Protocols

DDC Class

004: Informatik

Options

Loosely-stabilizing phase clocks and The Adaptive Majority Problem