{"paper":{"title":"Optimal Low-Degree Hardness of Maximum Independent Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR","stat.ML"],"primary_cat":"cs.CC","authors_text":"Alexander S. Wein","submitted_at":"2020-10-13T17:26:09Z","abstract_excerpt":"We study the algorithmic task of finding a large independent set in a sparse Erd\\H{o}s-R\\'{e}nyi random graph with $n$ vertices and average degree $d$. The maximum independent set is known to have size $(2 \\log d / d)n$ in the double limit $n \\to \\infty$ followed by $d \\to \\infty$, but the best known polynomial-time algorithms can only find an independent set of half-optimal size $(\\log d / d)n$. We show that the class of low-degree polynomial algorithms can find independent sets of half-optimal size but no larger, improving upon a result of Gamarnik, Jagannath, and the author. This generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06563","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06563/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"}