Stable Leader Election in Population Protocols Requires Linear Time

David Doty (1) , David Soloveichik (2)

1 UC Davis - University of California [Davis]
2 Computer Science Department [Austin]

A population protocol stably elects a leader if, for all n, starting from an initial configuration with n agents each in an identical state, with probability 1 it reaches a configuration y that is correct (exactly one agent is in a special leader state l) and stable (every configuration reachable from y also has a single agent in state l). We show that any population protocol that stably elects a leader requires Ω(n) expected “parallel time” — Ω(n^2) expected total pairwise interactions — to reach such a stable configuration. Our result also informs the understanding of the time complexity of chemical self-organization by showing an essential difficulty in generating exact quantities of molecular species quickly.

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]

David Doty, David Soloveichik. Stable Leader Election in Population Protocols Requires Linear Time. DISC 2015, Toshimitsu Masuzawa; Koichi Wada, Oct 2015, Tokyo, Japan. ⟨10.1007/978-3-662-48653-5_40⟩. ⟨hal-01207238⟩