{"paper":{"title":"The Andoni--Krauthgamer--Razenshteyn characterization of sketchable norms fails for sketchable metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.FA","math.MG"],"primary_cat":"cs.DS","authors_text":"Assaf Naor, Subhash Khot","submitted_at":"2018-10-10T00:56:59Z","abstract_excerpt":"Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC 2015) that a finite-dimensional normed space $(X,\\|\\cdot\\|_X)$ admits a $O(1)$ sketching algorithm (namely, with $O(1)$ sketch size and $O(1)$ approximation) if and only if for every $\\varepsilon\\in (0,1)$ there exist $\\alpha\\geqslant 1$ and an embedding $f:X\\to \\ell_{1-\\varepsilon}$ such that $\\|x-y\\|_X\\leqslant \\|f(x)-f(y)\\|_{1-\\varepsilon}\\leqslant \\alpha \\|x-y\\|_X$ for all $x,y\\in X$. The \"if part\" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04321","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"}