A stable majority population protocol using logarithmic time and states

12/31/2020
by   David Doty, et al.
0

We study population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied *majority* problem is that of determining in an initial population of n agents, each with one of two opinions A or B, whether there are more A, more B, or a tie. A *stable* protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of A, B, or T, from which the consensus cannot change. We describe a protocol that solves this problem using O(log n) states (loglog n + O(1) bits of memory) and optimal expected time O(log n). The number of states O(log n) is known to be optimal for the class of stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it state-optimal for that class. We use, and develop novel analysis of, a key technique called a "fixed resolution clock" due to Gasieniec, Stachowiak, and Uznanski, who showed a majority protocol using O(log n) time and states that has a positive probability of error. Our protocol is *nonuniform*: the transition function has the value ⌈log n⌉ encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to Θ(log n loglog n).

READ FULL TEXT

Authors

page 26

06/04/2021

A time and space optimal stable population protocol solving exact majority

We study population protocols, a model of distributed computing appropri...
06/24/2021

Self-Stabilizing Phase Clocks and the Adaptive Majority Problem

We present a self-stabilising phase clock for population protocols. In t...
12/31/2020

Consensus with Bounded Space and Minimal Communication

Population protocols are a fundamental model in distributed computing, w...
03/13/2020

Robust Comparison in Population Protocols

There has recently been a surge of interest in the computational and com...
03/22/2020

Distributed Computation with Continual Population Growth

Computing with synthetically modified bacteria is a vibrant and active f...
07/01/2018

Automatic Analysis of Expected Termination Time for Population Protocols

Population protocols are a formal model of sensor networks consisting of...
02/25/2022

Dynamic size counting in population protocols

The population protocol model describes a network of anonymous agents th...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.