{"paper":{"title":"Efficient Algorithms for Discrepancy Minimization in Convex Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.PR"],"primary_cat":"cs.DS","authors_text":"Mohit Singh, Ronen Eldan","submitted_at":"2014-09-09T22:50:21Z","abstract_excerpt":"A result of Spencer states that every collection of $n$ sets over a universe of size $n$ has a coloring of the ground set with $\\{-1,+1\\}$ of discrepancy $O(\\sqrt{n})$. A geometric generalization of this result was given by Gluskin (see also Giannopoulos) who showed that every symmetric convex body $K\\subseteq R^n$ with Gaussian measure at least $e^{-\\epsilon n}$, for a small $\\epsilon>0$, contains a point $y\\in K$ where a constant fraction of coordinates of $y$ are in $\\{-1,1\\}$. This is often called a partial coloring result. While both these results were inherently non-algorithmic, recently"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2913","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"}