{"paper":{"title":"Locality of not-so-weak coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DC","authors_text":"Alkida Balliu, Christoph Lenzen, Dennis Olivetti, Juho Hirvonen, Jukka Suomela","submitted_at":"2019-04-11T11:11:02Z","abstract_excerpt":"Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes:\n  - \"Easy\": solvable in $O(\\log^* n)$ rounds with both deterministic and randomized distributed algorithms.\n  - \"Hard\": requires at least $\\Omega(\\log n)$ rounds with deterministic and $\\Omega(\\log \\log n)$ rounds with ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05627","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}