{"paper":{"title":"Lossless Prioritized Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Ofer Neiman","submitted_at":"2019-07-16T13:29:02Z","abstract_excerpt":"Given metric spaces $(X,d)$ and $(Y,\\rho)$ and an ordering $x_1,x_2,\\ldots,x_n$ of $(X,d)$, an embedding $f: X \\rightarrow Y$ is said to have a prioritized distortion $\\alpha(\\cdot)$, if for any pair $x_j,x'$ of distinct points in $X$, the distortion provided by $f$ for this pair is at most $\\alpha(j)$. If $Y$ is a normed space, the embedding is said to have prioritized dimension $\\beta(\\cdot)$, if $f(x_j)$ may have nonzero entries only in its first $\\beta(j)$ coordinates.\n  The notion of prioritized embedding was introduced by \\cite{EFN15}, where a general methodology for constructing such em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06983","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"}