{"paper":{"title":"A O(1/eps^2)^n Time Sieving Algorithm for Approximate Integer Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Dadush","submitted_at":"2011-09-12T14:19:29Z","abstract_excerpt":"The Integer Programming Problem (IP) for a polytope P \\subseteq R^n is to find an integer point in P or decide that P is integer free. We give an algorithm for an approximate version of this problem, which correctly decides whether P contains an integer point or whether a (1+\\eps) scaling of P around its barycenter is integer free in time O(1/\\eps^2)^n. We reduce this approximate IP question to an approximate Closest Vector Problem (CVP) in a \"near-symmetric\" semi-norm, which we solve via a sieving technique first developed by Ajtai, Kumar, and Sivakumar (STOC 2001). Our main technical contrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2477","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":""},"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"}