New Clocks, Optimal Line Formation and Efficient Replication Population Protocols (Making Population Protocols Alive)

11/21/2021

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by   Leszek Gasieniec, et al.

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We consider the model of population protocols permitting presence of dynamically changing edges connecting agents. Our main contribution is a new constant space phase clock allowing to count parallel time O(nlog n) whp in the adopted model. This clock admits confirmation of slow leader election and in turn construction of a line (and a ring) comprising every agent in the optimal parallel time Θ(nlog n) and constant space. This improves on the currently best known upper bound O(n^2). We also discuss a variant of the new clock in which utilisation of edges is replaced by interaction of agents with a unique leader. This variant provides a universal (for models with and without edges) synchronisation mechanism and is adopted in some of our efficient line replication protocols.