{"paper":{"title":"Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Noah Stephens-Davidowitz","submitted_at":"2015-12-13T23:41:21Z","abstract_excerpt":"We show the first dimension-preserving search-to-decision reductions for approximate SVP and CVP. In particular, for any $\\gamma \\leq 1 + O(\\log n/n)$, we obtain an efficient dimension-preserving reduction from $\\gamma^{O(n/\\log n)}$-SVP to $\\gamma$-GapSVP and an efficient dimension-preserving reduction from $\\gamma^{O(n)}$-CVP to $\\gamma$-GapCVP. These results generalize the known equivalences of the search and decision versions of these problems in the exact case when $\\gamma = 1$. For SVP, we actually obtain something slightly stronger than a search-to-decision reduction---we reduce $\\gamma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04138","kind":"arxiv","version":5},"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"}