Abstract: We study here the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may have a few additional possible states and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in the initial majority. We first present and analyze a protocol with 4 states per vertex that always computes the initial majority value, under any fair scheduler. As we prove, this protocol is optimal, in the sense that there is no populat...
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Topics: 
Combinatorics
Discrete mathematics
Theoretical computer science