{"paper":{"title":"Fast Distance Oracles for Any Symmetric Norm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Omri Weinstein, Ruizhe Zhang, Yichuan Deng, Zhao Song","submitted_at":"2022-05-30T02:48:08Z","abstract_excerpt":"In the Distance Oracle problem, the goal is to preprocess $n$ vectors $x_1, x_2, \\cdots, x_n$ in a $d$-dimensional metric space $(\\mathbb{X}^d, \\| \\cdot \\|_l)$ into a cheap data structure, so that given a query vector $q \\in \\mathbb{X}^d$ and a subset $S\\subseteq [n]$ of the input data points, all distances $\\| q - x_i \\|_l$ for $x_i\\in S$ can be quickly approximated (faster than the trivial $\\sim d|S|$ query time). This primitive is a basic subroutine in machine learning, data mining and similarity search applications. In the case of $\\ell_p$ norms, the problem is well understood, and optimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14816","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.14816/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}