## Abstract

In population protocols, the underlying distributed network consists of n nodes (or agents), denoted by V, and a scheduler that continuously selects uniformly random pairs of nodes to interact. When two nodes interact, their states are updated by applying a state transition function that depends only on the states of the two nodes prior to the interaction. The efficiency of a population protocol is measured in terms of both time (which is the number of interactions until the nodes collectively have a valid output) and the number of possible states of nodes used by the protocol. By convention, we consider the parallel time cost, which is the time divided by n. In this paper we consider the majority problem, where each node receives as input a color that is either black or white, and the goal is to have all of the nodes output the color that is the majority of the input colors. We design a population protocol that solves the majority problem in O(log^{3/2} n) parallel time, both with high probability and in expectation, while using O(log n) states. Our protocol improves on a recent protocol of Berenbrink et al. that runs in O(log^{5/3} n) parallel time, both with high probability and in expectation, using O(log n) states.

Original language | English |
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Title of host publication | PODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 191-199 |

Number of pages | 9 |

ISBN (Electronic) | 9781450375825 |

DOIs | |

State | Published - 31 Jul 2020 |

Event | 39th Symposium on Principles of Distributed Computing, PODC 2020 - Virtual, Online, Italy Duration: 3 Aug 2020 → 7 Aug 2020 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 39th Symposium on Principles of Distributed Computing, PODC 2020 |
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Country/Territory | Italy |

City | Virtual, Online |

Period | 3/08/20 → 7/08/20 |

### Bibliographical note

Publisher Copyright:© 2020 ACM.

### Funding

∗Stav Ben-Nun, Tsvi Kopelowitz, Matan kraus and Ely Porat were supported by ISF grants no. 1278/16 and 1926/19, by a BSF grant 2018364, and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).

Funders | Funder number |
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Horizon 2020 Framework Programme | 683064 |

European Commission | |

United States-Israel Binational Science Foundation | 2018364 |

Israel Science Foundation | 1926/19, 1278/16 |

## Keywords

- majority
- population protocols

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