---
_id: '9951'
abstract:
- lang: eng
text: "There has recently been a surge of interest in the computational and complexity
properties of the population model, which assumes n anonymous, computationally-bounded
nodes, interacting at random, with the goal of jointly computing global predicates.
Significant work has gone towards investigating majority or consensus dynamics
in this model: that is, assuming that every node is initially in one of two states
X or Y, determine which state had higher initial count.\r\n\r\nIn this paper,
we consider a natural generalization of majority/consensus, which we call comparison
: in its simplest formulation, we are given two baseline states, X and Y, present
in any initial configuration in fixed, but possibly small counts. One of these
states has higher count than the other: we will assume |X_0| > C |Y_0| for some
constant C > 1. The challenge is to design a protocol by which nodes can quickly
and reliably decide on which of the baseline states X_0 and Y_0 has higher initial
count. We begin by analyzing a simple and general dynamics solving the above comparison
problem, which uses O( log n ) states per node, and converges in O(log n) (parallel)
time, with high probability, to a state where the whole population votes on opinions
X or Y at rates proportional to the initial concentrations of |X_0| vs. |Y_0|.
We then describe how this procedure can be bootstrapped to solve comparison, i.e.
have every node in the population reach the \"correct'' decision, with probability
1 - o(1), at the cost of O (log log n) additional states. Further, we prove that
this dynamics is self-stabilizing, in the sense that it converges to the correct
decision from arbitrary initial states, and leak-robust, in the sense that it
can withstand spurious faulty reactions, which are known to occur in practical
implementations of population protocols. Our analysis is based on a new martingale
concentration result relating the discrete-time evolution of a population protocol
to its expected (steady-state) analysis, which should be a useful tool when analyzing
opinion dynamics and epidemic dissemination in the population model."
acknowledgement: We would like to thank Rati Gelashvili for very useful discussions,
and the PODC anonymous reviewers for their careful reading of our paper, and for
their useful remarks. This work is partially supported by the Polish National Science
Center (NCN) grant UMO2017/25/B/ST6/02010.
article_processing_charge: No
author:
- first_name: Dan-Adrian
full_name: Alistarh, Dan-Adrian
id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
last_name: Alistarh
orcid: 0000-0003-3650-940X
- first_name: Martin
full_name: Töpfer, Martin
id: 4B865388-F248-11E8-B48F-1D18A9856A87
last_name: Töpfer
- first_name: Przemysław
full_name: Uznański, Przemysław
last_name: Uznański
citation:
ama: 'Alistarh D-A, Töpfer M, Uznański P. Comparison dynamics in population protocols.
In: *Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing*.
Association for Computing Machinery; 2021:55-65. doi:10.1145/3465084.3467915'
apa: 'Alistarh, D.-A., Töpfer, M., & Uznański, P. (2021). Comparison dynamics
in population protocols. In *Proceedings of the 2021 ACM Symposium on Principles
of Distributed Computing* (pp. 55–65). Virtual, Italy: Association for Computing
Machinery. https://doi.org/10.1145/3465084.3467915'
chicago: Alistarh, Dan-Adrian, Martin Töpfer, and Przemysław Uznański. “Comparison
Dynamics in Population Protocols.” In *Proceedings of the 2021 ACM Symposium
on Principles of Distributed Computing*, 55–65. Association for Computing Machinery,
2021. https://doi.org/10.1145/3465084.3467915.
ieee: D.-A. Alistarh, M. Töpfer, and P. Uznański, “Comparison dynamics in population
protocols,” in *Proceedings of the 2021 ACM Symposium on Principles of Distributed
Computing*, Virtual, Italy, 2021, pp. 55–65.
ista: 'Alistarh D-A, Töpfer M, Uznański P. 2021. Comparison dynamics in population
protocols. Proceedings of the 2021 ACM Symposium on Principles of Distributed
Computing. PODC: Symposium on Principles of Distributed Computing, 55–65.'
mla: Alistarh, Dan-Adrian, et al. “Comparison Dynamics in Population Protocols.”
*Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing*,
Association for Computing Machinery, 2021, pp. 55–65, doi:10.1145/3465084.3467915.
short: D.-A. Alistarh, M. Töpfer, P. Uznański, in:, Proceedings of the 2021 ACM
Symposium on Principles of Distributed Computing, Association for Computing Machinery,
2021, pp. 55–65.
conference:
end_date: 2021-07-30
location: Virtual, Italy
name: 'PODC: Symposium on Principles of Distributed Computing'
start_date: 2021-07-26
date_created: 2021-08-22T22:01:20Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2023-08-11T10:56:04Z
day: '21'
department:
- _id: DaAl
doi: 10.1145/3465084.3467915
external_id:
isi:
- '000744439800005'
isi: 1
language:
- iso: eng
month: '07'
oa_version: None
page: 55-65
publication: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing
publication_identifier:
isbn:
- '9781450385480'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Comparison dynamics in population protocols
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...