Counting with Population Protocols

Yves Mocquard (1) , Emmanuelle Anceaume (2) , James Aspnes (3) , Yann Busnel (4, 5) , Bruno Sericola (4)

1 UR - Université de Rennes
2 CIDRE - Confidentialité, Intégrité, Disponibilité et Répartition
3 YALE - Department of Computer Science
4 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
5 ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz]

The population protocol model provides theoretical foundations for analyzing the properties emerging from simple and pairwise interactions among a very large number n of anonymous agents. The problem tackled in this paper is the following one: is there an efficient population protocol that exactly counts the difference κ between the number of agents that initially and independently set their state to A and the one that initially set it to B, assuming that each agent only uses a finite set of states ? We propose a solution which guarantees with any high probability that after O(log n) interactions any agent outputs the exact value of κ. Simulation results illustrate our theoretical analysis.

Mots clés: Majority algorithm; Counting problem; Performance evaluation; Population protocol

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

Yves Mocquard, Emmanuelle Anceaume, James Aspnes, Yann Busnel, Bruno Sericola. Counting with Population Protocols. 2015 IEEE 14th International Symposium on Network Computing and Applications, IEEE, Sep 2015, Cambridge, United States. pp.9, ⟨10.1109/nca.2015.35⟩. ⟨hal-01189596⟩