Fast space optimal leader election in population protocols

Leszek Gasieniec, Grzegorz Stachowiak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

50 Scopus citations


The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions from the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol operates in parallel time O(log2 n) equivalent to O(n log2 n) sequential pairwise interactions, in which each agent utilises O(log log n) states. This double logarithmic space utilisation matches asymptotically the lower bound 1 2 log log n on the number of states utilised by agents in any leader election algorithm with the running time o( n polylog n), see [7]. Our solution relies on the concept of phase clocks, a fundamental synchronisation and coordination tool in the field of Distributed Computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct and fast with high probability.

Original languageEnglish (US)
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Number of pages15
ISBN (Electronic)9781611975031
StatePublished - 2018
Externally publishedYes
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Country/TerritoryUnited States
CityNew Orleans

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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