{"paper":{"title":"Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Jara Uitto, Malte Baumecker, Rustam Latypov, Yannic Maus","submitted_at":"2026-06-10T11:53:00Z","abstract_excerpt":"Given a graph $G=(V,E)$, a $\\beta$-ruling set is a subset of nodes $S\\subseteq V$ that is independent, and each node in $V$ is at distance at most $\\beta$ from some node in $S$. In this paper, we present almost optimal distributed algorithms for finding $2$-ruling sets in the classical \\LOCAL model. Our main contribution is a randomized algorithm that w.h.p.\\ computes a $2$-ruling set on any $n$-node graph with bounded arboricity in $O(\\log \\log n)$ rounds. In fact, the algorithm works up to arboricity $O(\\log\\log n)$, improves exponentially over the prior state of the art that can be achieved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11974","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11974/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}