## Abstract

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the [Θ(log n), Θ(n)] region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in O(log n) rounds. If not, it is known that the complexity has to be Θ(n^{1/k}) for some k = 1, 2, ..., and in this case the algorithms also output the right value of the exponent k.

In rooted trees in the O(log n) case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the O(log n) region remains an open question.

In rooted trees in the O(log n) case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the O(log n) region remains an open question.

Original language | English |
---|---|

Title of host publication | 36th International Symposium on Distributed Computing (DISC 2022) |

Editors | Christian Scheideler |

Publisher | Schloss Dagstuhl-Leibniz-Zentrum für Informatik |

Chapter | 8 |

Pages | 1-19 |

ISBN (Electronic) | 978-3-95977-255-6 |

DOIs | |

Publication status | Published - 2022 |

MoE publication type | A4 Article in a conference publication |

Event | International Symposium on Distributed Computing - Augusta, United States Duration: 25 Oct 2022 → 27 Oct 2022 Conference number: 36 |

### Publication series

Name | Leibniz International Proceedings in Informatics (LIPIcs) |
---|---|

Publisher | Schloss Dagstuhl--Leibniz-Zentrum für Informatik |

Volume | 246 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | International Symposium on Distributed Computing |
---|---|

Abbreviated title | DISC |

Country/Territory | United States |

City | Augusta |

Period | 25/10/2022 → 27/10/2022 |