## Abstract

Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are examples of LCLs. On the one hand, it is known that some LCLs benefit exponentially from randomness - -for example, any deterministic distributed algorithm that finds a sinkless orientation requires Θ(log n) rounds in the LOCAL model, while the randomized complexity of the problem is Θ(log log n) rounds. On the other hand, there are also many LCLs in which randomness is useless. Previously, it was not known whether there are any LCLs that benefit from randomness, but only subexponentially. We show that such problems exist: for example, there is an LCL with deterministic complexity Θ(log^{2} n) rounds and randomized complexity Θ(log n log log n) rounds.

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

Publisher | ACM |

Pages | 299-308 |

Number of pages | 10 |

ISBN (Electronic) | 9781450375825 |

DOIs | |

Publication status | Published - 31 Jul 2020 |

MoE publication type | A4 Article in a conference publication |

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

### Conference

Conference | ACM Symposium on Principles of Distributed Computing |
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Abbreviated title | PODC |

Country | Italy |

City | Virtual, Online |

Period | 03/08/2020 → 07/08/2020 |

## Keywords

- distributed computational complexity
- LOCAL model
- locally checkable labeling problems