{"paper":{"title":"Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Angelika Steger, Dan Hefetz, Fabian Kuhn, Yannic Maus","submitted_at":"2016-07-18T17:30:53Z","abstract_excerpt":"We show an $\\Omega\\big(\\Delta^{\\frac{1}{3}-\\frac{\\eta}{3}}\\big)$ lower bound on the runtime of any deterministic distributed $\\mathcal{O}\\big(\\Delta^{1+\\eta}\\big)$-graph coloring algorithm in a weak variant of the \\LOCAL\\ model.\n  In particular, given a network graph \\mbox{$G=(V,E)$}, in the weak \\LOCAL\\ model nodes communicate in synchronous rounds and they can use unbounded local computation. We assume that the nodes have no identifiers, but that instead, the computation starts with an initial valid vertex coloring. A node can \\textbf{broadcast} a \\textbf{single} message of \\textbf{unbounded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05212","kind":"arxiv","version":2},"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"}