{"paper":{"title":"Tighter inapproximability for set cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David G. Harris","submitted_at":"2016-12-06T00:53:00Z","abstract_excerpt":"Set Cover is a classic NP-hard problem; as shown by Slav\\'{i}k (1997) the greedy algorithm gives an approximation ratio of $\\ln n - \\ln \\ln n + \\Theta(1)$. A series of works by Lund \\& Yannakakis (1994), Feige (1998), Moshkovitz (2015) have shown that, under the assumption $P \\neq NP$, it is impossible to obtain a polynomial-time approximation ratio with approximation ratio $(1 - \\alpha) \\ln n$, for any constant $\\alpha > 0$.\n  In this note, we show that under the Exponential Time Hypothesis (a stronger complexity-theoretic assumptions than $P \\neq NP$), there are no polynomial-time algorithms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01610","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":""},"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"}