{"paper":{"title":"Factorization Norms and Hereditary Discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS"],"primary_cat":"math.CO","authors_text":"Aleksandar Nikolov, Jiri Matousek, Kunal Talwar","submitted_at":"2014-08-06T18:59:10Z","abstract_excerpt":"The $\\gamma_2$ norm of a real $m\\times n$ matrix $A$ is the minimum number $t$ such that the column vectors of $A$ are contained in a $0$-centered ellipsoid $E\\subseteq\\mathbb{R}^m$ which in turn is contained in the hypercube $[-t, t]^m$. We prove that this classical quantity approximates the \\emph{hereditary discrepancy} $\\mathrm{herdisc}\\ A$ as follows: $\\gamma_2(A) = {O(\\log m)}\\cdot \\mathrm{herdisc}\\ A$ and $\\mathrm{herdisc}\\ A = O(\\sqrt{\\log m}\\,)\\cdot\\gamma_2(A) $. Since $\\gamma_2$ is polynomial-time computable, this gives a polynomial-time approximation algorithm for hereditary discrepa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1376","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"}