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Stable Leader Election in Population Protocols Requires Linear Time

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Distributed Computing (DISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9363))

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Abstract

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 \(\ell \)) and stable (every configuration reachable from y also has a single agent in state \(\ell \)). We show that any population protocol that stably elects a leader requires \(\Omega (n)\) expected “parallel time” — \(\Omega (n^2)\) 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.

D. Doty—Author was supported by NSF grants CCF-1219274 and CCF-1442454 and the Molecular Programming Project under NSF grant 1317694.

D. Soloveichik—Author was supported by an NIGMS Systems Biology Center grant P50 GM081879 and NSF grant CCF-1442454.

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Correspondence to David Soloveichik .

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Doty, D., Soloveichik, D. (2015). Stable Leader Election in Population Protocols Requires Linear Time. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_40

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  • DOI: https://doi.org/10.1007/978-3-662-48653-5_40

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