{"paper":{"title":"$2^{\\log^{1-\\eps} n}$ Hardness for Closest Vector Problem with Preprocessing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Nisheeth K. Vishnoi, Preyas Popat, Subhash Khot","submitted_at":"2011-09-10T00:00:21Z","abstract_excerpt":"We prove that for an arbitrarily small constant $\\eps>0,$ assuming NP$\\not \\subseteq$DTIME$(2^{{\\log^{O(1/\\eps)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\\log ^{1-\\eps}n}.$ This improves upon the previous hardness factor of $(\\log n)^\\delta$ for some $\\delta > 0$ due to \\cite{AKKV05}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2176","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":""},"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"}