Efficient Classification of Locally Checkable Problems in Regular Trees

Alkida Balliu, Sebastian Brandt, Yi-Jun Chang, Dennis Olivetti, Jan Studený, Jukka Suomela

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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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.
Original languageEnglish
Title of host publication36th International Symposium on Distributed Computing (DISC 2022)
EditorsChristian Scheideler
PublisherSchloss Dagstuhl-Leibniz-Zentrum für Informatik
Chapter8
Pages1-19
ISBN (Electronic)978-3-95977-255-6
DOIs
Publication statusPublished - 2022
MoE publication typeA4 Article in a conference publication
EventInternational Symposium on Distributed Computing - Augusta, United States
Duration: 25 Oct 202227 Oct 2022
Conference number: 36

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Volume246
ISSN (Print)1868-8969

Conference

ConferenceInternational Symposium on Distributed Computing
Abbreviated titleDISC
Country/TerritoryUnited States
CityAugusta
Period25/10/202227/10/2022

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