Optimal Proportion Computation with Population Protocols

Yves Mocquard 1, * Emmanuelle Anceaume 2 Bruno Sericola 3
* Corresponding author
2 CIDRE - Confidentialité, Intégrité, Disponibilité et Répartition
CentraleSupélec, Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
3 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
Abstract : The computational model of population protocols is a formalism that allows the analysis of properties emerging from simple and pairwise interactions among a very large number of anonymous finite-state agents. Significant work has been done so far to determine which problems are solvable in this model and at which cost in terms of states used by the protocols and time needed to converge. The problem tackled in this paper is the population proportion problem: each agent starts independently from each other in one of two states, say A or B, and the objective is for each agent to determine the proportion of agents that initially started in state A, assuming that each agent only uses a finite set of state, and does not know the number n of agents. We propose a solution which guarantees with any high probability that after O(log n) interactions any agent outputs with a precision given in advance, the proportion of agents that start in state A. The population proportion problem is a generalization of both the majority and counting problems, and thus our solution solves both problems. We show that our solution is optimal in time and space. Simulation results illustrate our theoretical analysis.
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Yves Mocquard, Emmanuelle Anceaume, Bruno Sericola. Optimal Proportion Computation with Population Protocols. Symposium on Network Computing and Applications, IEEE, Oct 2016, Boston, United States. ⟨hal-01354352v2⟩

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