{"paper":{"title":"Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Konrad, Viktor Zamaraev","submitted_at":"2018-05-11T18:21:02Z","abstract_excerpt":"We give deterministic distributed $(1+\\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\\frac{1}{\\epsilon} \\log n)$ rounds, and our independent set algorithm has a runtime of $O(\\frac{1}{\\epsilon}\\log(\\frac{1}{\\epsilon})\\log^* n)$ rounds. For coloring, existing lower bounds imply that the dependencies on $\\frac{1}{\\epsilon}$ and $\\log n$ are best possible. For independent set, we prove that $O(\\frac{1}{\\epsilon})$ rounds are necessary.\n  Both our algorithms make use of a tree decom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04544","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"}