{"paper":{"title":"Near-Optimal Deterministic Network Decomposition and Ruling Set, and Improved MIS","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Christoph Grunau, Mohsen Ghaffari","submitted_at":"2024-10-25T12:41:04Z","abstract_excerpt":"This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three decades:\n  Near-Optimal Network Decomposition: We present a deterministic distributed algorithm that computes a network decomposition in approximately O(log^2 n) rounds, with O(log n) diameter and O(log n) colors. This round complexity is near-optimal in the following sense: even given an ideal network decomposition, using it (in the standard way) requires round c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19516","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/2410.19516/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"}