# Efficient classification of local problems in regular trees

DISC 2022 · 36th International Symposium on Distributed Computing, Augusta, GA, USA, October 2022 ·

# Abstract

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ 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 $\Theta(n^{1/k})$ for some $k = 1, 2, \dotsc$, 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.

# Publication

Christian Scheideler (Ed.): 36th International Symposium on Distributed Computing (DISC 2022), volume 246 of Leibniz International Proceedings in Informatics (LIPIcs), pages 8:1–8:19, Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2022

ISBN 978-3-95977-255-6

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