Population Protocols with Convergence Detection

Yves Mocquard (1) , Bruno Sericola (1) , Emmanuelle Anceaume (2)

1 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
2 CIDRE - Confidentialité, Intégrité, Disponibilité et Répartition

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.

Mots clés: Detection of convergence; Anonymous agents; Population protocols; Large scale systems; Probabilistic analysis

Domaines: Informatique [cs]; Algorithme et structure de données [cs.DS]; Calcul parallèle, distribué et partagé [cs.DC]

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⟩