{"paper":{"title":"Almost Global Problems in the LOCAL Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Alkida Balliu, Dennis Olivetti, Jukka Suomela, Sebastian Brandt","submitted_at":"2018-05-12T20:25:59Z","abstract_excerpt":"The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in bounded-degree graphs, the following picture emerges:\n  - There are lots of problems with time complexities of $\\Theta(\\log^* n)$ or $\\Theta(\\log n)$.\n  - It is not possible to have a problem with complexity between $\\omega(\\log^* n)$ and $o(\\log n)$.\n  - In general graphs, we can construct LCL problems with infinitely many complexities between $\\omega(\\log n)$ and $n^{o(1)}$.\n  - In tre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04776","kind":"arxiv","version":3},"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/1805.04776/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"}