{"paper":{"title":"Data-Dependent LSH for the Earth Mover's Distance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Erik Waingarten, Rajesh Jayaram, Tian Zhang","submitted_at":"2024-03-08T04:35:55Z","abstract_excerpt":"We give new data-dependent locality sensitive hashing schemes (LSH) for the Earth Mover's Distance ($\\mathsf{EMD}$), and as a result, improve the best approximation for nearest neighbor search under $\\mathsf{EMD}$ by a quadratic factor. Here, the metric $\\mathsf{EMD}_s(\\mathbb{R}^d,\\ell_p)$ consists of sets of $s$ vectors in $\\mathbb{R}^d$, and for any two sets $x,y$ of $s$ vectors the distance $\\mathsf{EMD}(x,y)$ is the minimum cost of a perfect matching between $x,y$, where the cost of matching two vectors is their $\\ell_p$ distance. Previously, Andoni, Indyk, and Krauthgamer gave a (data-in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05041","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/2403.05041/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"}