{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-classification-of-local-problems-in","title":"Efficient Classification of Locally Checkable Problems in Regular Trees","arxiv_id":"2202.08544","date":"2022-02-17","proceeding":null,"authors":["Alkida Balliu","Sebastian Brandt","Yi-Jun Chang","Dennis Olivetti","Jan Studený","Jukka Suomela"],"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.","url_abs":"https://arxiv.org/abs/2202.08544v2","url_pdf":"https://arxiv.org/pdf/2202.08544v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-classification-of-local-problems-in","repo_url":"https://github.com/jendas1/poly-classifier","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}