eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-10-17
8:1
8:19
10.4230/LIPIcs.DISC.2022.8
article
Efficient Classification of Locally Checkable Problems in Regular Trees
Balliu, Alkida
1
Brandt, Sebastian
2
Chang, Yi-Jun
3
Olivetti, Dennis
1
Studený, Jan
4
Suomela, Jukka
4
Gran Sasso Science Institute, L'Aquila, Italy
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
National University of Singapore, Singapore
Aalto University, Espoo, Finland
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol246-disc2022/LIPIcs.DISC.2022.8/LIPIcs.DISC.2022.8.pdf
locally checkable labeling
locality
distributed computational complexity