# Population Protocols with Convergence Detection

1 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA_D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
2 CIDRE - Confidentialité, Intégrité, Disponibilité et Répartition
CentraleSupélec, Inria Rennes – Bretagne Atlantique , IRISA_D1 - SYSTÈMES LARGE ÉCHELLE
Abstract : This paper focuses on pairwise interaction-based protocols, and proposes an universal mechanism that allows each agent to locally detect that the system has converged to the sought configuration with high probability. To illustrate our mechanism, we use it to detect the instant at which the proportion problem is solved. Specifically, let nA (resp. nB) be the number of agents that initially started in state A (resp. B) and $γA = nA/n$, where n is the total number of agents. Our protocol guarantees, with a given precision $ε > 0$ and any high probability $1 − δ$, that after $O(n ln(n/δ))$ interactions, any queried agent that has set the detection flag will output the correct value of the proportion γA of agents which started in state A, by maintaining no more than $O(ln(n)/ε)$ integers. We are not aware of any such results. Simulation results illustrate our theoretical analysis.
Keywords :
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01849441
Contributor : Emmanuelle Anceaume <>
Submitted on : Thursday, July 26, 2018 - 11:19:46 AM
Last modification on : Thursday, February 7, 2019 - 5:08:02 PM
Long-term archiving on : Saturday, October 27, 2018 - 1:27:18 PM

### File

main.pdf
Files produced by the author(s)

### Citation

Yves Mocquard, Bruno Sericola, Emmanuelle Anceaume. Population Protocols with Convergence Detection. NCA 2018 - 17th IEEE International Symposium on Network Computing and Applications (NCA), Nov 2018, Boston, United States. pp.1-8, ⟨10.1109/NCA.2018.8548344⟩. ⟨hal-01849441⟩

Record views