Probabilistic Analysis of Counting Protocols in Large-scale Asynchronous and Anonymous Systems

Yves Mocquard 1 Bruno Sericola 1 Emmanuelle Anceaume 2
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 : We consider a large system populated by n anonymous nodes that communicate through asynchronous and pair-wise interactions. The aim of these interactions is for each node to converge toward a global property of the system, that depends on the initial state of each node. In this paper we focus on both the counting and proportion problems. We show that for any δ ∈ (0, 1), the number of interactions per node is O(ln(n/δ)) with probability at least 1 − δ. We also prove that each node can determine, with any high probability, the proportion of nodes that initially started in a given state without knowing the number of nodes in the system. This work provides a precise analysis of the convergence bounds, and shows that using the 4-norm is very effective to derive useful bounds.
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Yves Mocquard, Bruno Sericola, Emmanuelle Anceaume. Probabilistic Analysis of Counting Protocols in Large-scale Asynchronous and Anonymous Systems. Proceedings of the 16th IEEE International Conference on Network Computing and Applications, Oct 2017, Boston, United States. ⟨hal-01580275v3⟩

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