{"paper":{"title":"Finding an Integral vector in an Unknown Polyhedral Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ali Kakhbod, Morteza Zadimoghaddam","submitted_at":"2010-01-31T10:59:06Z","abstract_excerpt":"We present an algorithm to find an integral vector in the polyhedral cone $\\Gamma=\\{X | \\textbf{A}X \\leq \\textbf{0}\\}$, without assuming the explicit knowledge of $\\textbf{A}$. About the polyhedral cone, $\\Gamma$, it is only given that, (i) the elements of \\textbf{A} are in $\\{-d,-d+1,\\...,0,\\...,d-1,d\\}$, $d \\in \\mathbb{N}$, and, (ii) $Y=[y(1),y(2),\\...,y(n)]$ is a non-zero integral solution to $\\Gamma$. The proposed algorithm finds a non-zero integral vector in $\\Gamma$ such that its maximum element is less than ${(2d)^{2^{n-1}-1}}/{2^{n-1}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0117","kind":"arxiv","version":4},"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"}