A time and space optimal stable population protocol solving exact majority

06/04/2021
βˆ™
by   David Doty, et al.
βˆ™
0
βˆ™

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, 𝖑, 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 polylogarithmic time stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-optimal for that class. We introduce a key technique called a "fixed resolution clock" to achieve partial synchronization. Our protocol is *nonuniform*: the transition function has the value ⌈log nβŒ‰ 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

βˆ™ 12/31/2020

A stable majority population protocol using logarithmic time and states

We study population protocols, a model of distributed computing appropri...
βˆ™ 11/14/2020

Time and Space Optimal Exact Majority Population Protocols

In this paper we study population protocols governed by the random sched...
βˆ™ 06/24/2021

Self-Stabilizing Phase Clocks and the Adaptive Majority Problem

We present a self-stabilising phase clock for population protocols. In t...
βˆ™ 03/13/2020

Robust Comparison in Population Protocols

There has recently been a surge of interest in the computational and com...
βˆ™ 05/10/2021

ppsim: A software package for efficiently simulating and visualizing population protocols

We introduce ppsim, a software package for efficiently simulating popula...
βˆ™ 02/25/2022

Dynamic size counting in population protocols

The population protocol model describes a network of anonymous agents th...
βˆ™ 01/11/2021

Running Time Analysis of Broadcast Consensus Protocols

Broadcast consensus protocols (BCPs) are a model of computation, in whic...
This week in AI

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